Math POTW for Secondary and High School Students Forum

POTW Inequality of Positive Real Numbers: Proving (1-1/x^2)(1-1/y^2)≥9 with x+y≤1
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12
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1K
POTW Integer n: Solving the Equation ##\dfrac{n^2+3}{2n+4}## for Integers
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14
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1K
POTW Solve 3-Variable Equation with Real Solutions | √(z-y^2-6x-26)+x^2+6y+z-8=0
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3
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899
MHB How Can You Minimize This Complex Square Root Expression for Positive x and y?
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6
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1K
POTW Prove that the roots of a polynomial cannot be all real
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5
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1K
MHB Can x(x+y) Be Proved to Be ≤ 2 for Positive Real Numbers?
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11
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1K
POTW Proving Inequality between Positive Real Numbers a and b: a(a+b) ≤ 2
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6
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973
MHB Maximize (x1+x2)(x1+x3)x4 for Quartic Equation with Real Roots in [1/2,2]
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2
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982
POTW Find Triplets of Positive Integers with Sum of Cubes
2
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66
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3K
MHB Can You Verify This Trigonometric Identity Involving Cosecant Functions?
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1
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962
MHB What Is the Minimum Value of (a²+b²)/c² in Triangle ABC?
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1
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903
POTW Find the Sum of Two Real Numbers | Solve a + b with Given Equations
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19
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1K
MHB Is the product of two radical expressions equal to six?
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13
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1K
POTW Finding the Product of Real Roots: POTW Equation Solution
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9
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1K
MHB What Is the Maximum Value of \( x \) in the Equation \( 2x+y+\frac{4}{xy}=10 \)?
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7
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1K
MHB What Is the Minimum Cosine Value in Trigonometric Constraints?
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2
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932
MHB How Can We Find All Integer Pairs (k, n) That Satisfy This Factorial Equation?
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4
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1K
MHB What is the minimum value of a+b+c+d if a^2-b^2+cd^2=2022?
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5
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1K
MHB Minimum Value of (a+7)^2+(b+2)^2 with Constraint (a-5)^2+(b-7)^2=4 - POTW #506
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5
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930
MHB Minimum Sum of Non-Negative Integers with Given Equation - POTW #504
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1
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814
MHB Can $\sin^5 x + \cos^3 x$ Equal 1?
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1
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1K
MHB Can This Infinite Product Surpass 50?
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1
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804
MHB Can This Triangle Configuration Prove a Right Angle?
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1
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894
MHB Can You Prove the Polynomial Has Three Distinct Roots?
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1
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747
MHB Can $2^{\sqrt{12}}$ Exceed 11?
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2
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949
MHB What is the Range of $w(w+x)(w+y)(w+z)$ When $x+y+z+w=x^7+y^7+z^7+w^7=0$?
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1
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837
MHB Can Both Solutions of This Quadratic Equation Be Perfect Squares?
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1
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851
MHB How many positive integral solutions $(x,\,y)$ are there for the equation $\dfrac{1}{x+1}+\dfrac{1}{y}+\dfrac{1}{y(x+1)}=\dfrac{1}{2015}$?
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1
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801
MHB What is the greatest 5-digit palindrome for 7n to be a 6-digit palindrome?
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1
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798
MHB How do you solve a system of equations with rational functions?
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1
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997
MHB Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
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1
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817
MHB Can You Simplify This Trigonometric Expression?
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1
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752
MHB How Does Solving P(x) Influence Q(x^2)?
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1
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770
MHB Can You Prove This Inequality with Positive Real Numbers?
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1
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873
MHB How Do You Evaluate the Product of g(x) at the Roots of a Quintic Polynomial?
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1
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780
MHB Sum of Cosine Values for $x$ | POTW #480 8/24/2021 | $100^{\circ}<x<200^{\circ}$
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1
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945
MHB What is the value of (x+y)(y+z)(z+x) if 1/(x+y+z) = 1/x + 1/y + 1/z?
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1
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835
MHB Find All Positive Integer Pairs for (x, y) in sqrt[3]{7x^2-13xy+7y^2}=|x-y|+1
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1
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864
MHB How to Evaluate the Expression for Roots of the Polynomial in POTW #476?
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1
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830
MHB What is the solution for evaluating $ab+cd$ with given constraints in POTW #477?
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1
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766
MHB Can You Solve This Unique Fraction Challenge?
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1
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819
MHB Can you solve this week's POTW #474: Four real numbers with unique permutations?
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1
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869
MHB What Is the Largest Natural Number $n$ Such That $2^n$ Divides $3^{2016}-1$?
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1
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942
MHB Discover the Area of Points in a Unit Square | POTW #471
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1
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774
MHB How Many Integer Solutions Exist for the Equation |x|+|y|+|z|=2010?
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2
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788
MHB Prove Inequality: Integral of Square Root vs. Trigonometric Function
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1
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839
MHB Find Functions Satisfying $f^d(x)=2015-x$ for All Divisors of 2015
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1
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776
MHB Can $(n^2+11n-4) \cdot n! + 33 \cdot 13^n + 4$ Be a Perfect Square?
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2
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813
MHB What is the Time Estimate for Completing a 1000-Piece Jigsaw Puzzle?
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1
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895
MHB Finding Extremes of x^3+y^3+z^3+xyz for Real Numbers with Constraints
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1
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756
MHB Can You Solve This Week's Challenging System of Equations?
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1
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832
MHB Which Prime Numbers Make $2p^3 + 4p^2 - 3p + 12$ a Fifth Power?
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1
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1K
MHB Is Every Positive Real Number a Solution to (x+1)(x+2)(x+5)≥36x?
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1
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890
MHB What Are the Possible Values of c for a Triangle with Area 5?
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1
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751
MHB Can All Outputs of a Quadratic Function Be Integers?
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1
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857
MHB Can Non-zero Polynomials with Real Coefficients Have Real Roots in Common?
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1
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889
MHB Is it possible to find 6-digit numbers with a sum of 8?
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1
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909
MHB Possible Values: $f(8765)-f(4321)$ for Functions Satisfying Inequalities
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1
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783
MHB How Do You Solve POTW #456 for (x+20)(y+20)(z+20)?
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1
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815
MHB Can You Solve the Integer System xz-2yt=3 and xt+yz=1?
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1
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937
MHB What is the Greatest Value of an Expression with Given Numbers and Equation?
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1
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872
MHB Integer Solutions for Equation: POTW #453 - Feb 1st, 2021
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1
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928
MHB Can You Solve This Integer Equation for January 25th, 2021?
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3
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926
MHB How Many Divisors of $30^{2003}$ Are Not Divisors of $20^{2000}$?
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1
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836
MHB What are the solutions to x^3+3367=2^n?
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1
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1K
MHB Triangle ABC: Find Possible Values of Cos A | POTW #449 Jan 4th 2021
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2
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835
MHB How to Tackle the Latest POTW Inequality Challenge?
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2
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876
MHB Can You Solve for a and b in This Trigonometric Equation?
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1
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771
MHB Triangle with Complex Number Vertices SATISFIES Equilateral Relation
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1
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892
MHB Proof of Regular Heptagon Ratio: AD^3/AB^3 - (AB+2AC)/(AD-AC) = 1
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1
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868
MHB Maximum Value of Square Root Expression with Three Variables in [0,1]
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2
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1K
MHB How Many Non-Congruent Triangles with Integer Sides Can a Given Perimeter Form?
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1
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862
MHB Is Sine of x Greater Than or Equal to 2x Over Pi for Angles Up to Pi/2?
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1
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877
MHB Can You Solve the Convex Quadrilateral Angle Mystery?
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2
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987
MHB Can All Roots of This Cubic Equation Be Bounded by 1?
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1
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845
MHB Is the Expression an Integer When Rational Conditions Apply?
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1
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810
MHB Can You Prove These Inequalities for Real Numbers a, b, and c?
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2
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900
MHB What are the solutions to a set of equations involving triple real numbers and specific conditions?
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1
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889
MHB Is It Possible to Prove Real Root Properties in Cubic Equations?
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1
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959
MHB What Is the Value of b If All Roots of the Polynomial Are Positive Real Numbers?
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2
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893
MHB Quadratic Polynomial Problem: Proving Equality with Real Numbers
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1
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898
MHB Solution to Problem #433: Proving a+b+c=0 yields 9
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1
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854
MHB How Many Final Points Can Be Reached in a Ten-Step Lattice Walk?
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1
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868
MHB How Do Divisors Relate in POTW #431's Integer Equation?
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1
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964
MHB Which Integers Make All Roots of This Polynomial Integer?
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1
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868
MHB How Do You Calculate the Sum of Sides and Diagonals of a Regular 12-Gon?
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1
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870
MHB How Can a Fifth Degree Polynomial Meet Specific Divisibility Conditions?
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2
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952
MHB Challenge: Find the Positive Integer for $133^5$ + $110^5$ + $84^5$ + $27^5$
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1
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1K
MHB The value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$ is 1234.
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1
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911
MHB Can You Solve This Complex Radical Equation?
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1
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890
MHB Maximizing a in $ax^3+bx^2+cx+d$ with Constraints | POTW #424 07/06/2020
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1
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978
MHB How to Calculate the Sum of Squares in Complex Equation Systems?
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1
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915
MHB Problem #422: Four Non-Negative Real Numbers and a Unique Condition
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1
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993
MHB What Natural Numbers Solve the Equation from POTW #421?
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1
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976
MHB Find the Sum of Real Numbers Satisfying Equations
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1
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969
MHB What Is the Probability That a Bridge Is Empty at Noon?
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1
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967
MHB Can you solve this week's POTW: Integrating a Complex Expression? May 25th, 2020
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1
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945
MHB Acute Triangle ABC: Point P and Line Intersections Formula
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1
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849
MHB Can You Solve These Unique System of Equations?
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1
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1K
MHB How Can One Non-Real Root Be Guaranteed in Equation #416?
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1
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1K
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POTW High School

Welcome to the High School POTW forum!

Math problems will be posted each week on Monday, most likely early in the morning (1am, 2am, etc.) Eastern Standard Time. There will be one math problem each week at the advanced high school student or secondary level.

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