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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883
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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942
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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953
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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938
MHB What Is the Minimum Value of (a²+b²)/c² in Triangle ABC?
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1
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886
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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914
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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905
MHB Minimum Sum of Non-Negative Integers with Given Equation - POTW #504
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1
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794
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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784
MHB Can This Triangle Configuration Prove a Right Angle?
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1
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874
MHB Can You Prove the Polynomial Has Three Distinct Roots?
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1
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698
MHB Can $2^{\sqrt{12}}$ Exceed 11?
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2
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929
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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825
MHB Can Both Solutions of This Quadratic Equation Be Perfect Squares?
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1
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832
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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767
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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776
MHB How do you solve a system of equations with rational functions?
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1
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963
MHB Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
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1
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791
MHB Can You Simplify This Trigonometric Expression?
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1
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735
MHB How Does Solving P(x) Influence Q(x^2)?
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1
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750
MHB Can You Prove This Inequality with Positive Real Numbers?
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1
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842
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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763
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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918
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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797
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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841
MHB How to Evaluate the Expression for Roots of the Polynomial in POTW #476?
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1
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812
MHB What is the solution for evaluating $ab+cd$ with given constraints in POTW #477?
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1
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748
MHB Can You Solve This Unique Fraction Challenge?
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1
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796
MHB Can you solve this week's POTW #474: Four real numbers with unique permutations?
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1
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828
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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923
MHB Discover the Area of Points in a Unit Square | POTW #471
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1
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756
MHB How Many Integer Solutions Exist for the Equation |x|+|y|+|z|=2010?
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2
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765
MHB Prove Inequality: Integral of Square Root vs. Trigonometric Function
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1
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753
MHB Find Functions Satisfying $f^d(x)=2015-x$ for All Divisors of 2015
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1
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757
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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794
MHB What is the Time Estimate for Completing a 1000-Piece Jigsaw Puzzle?
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1
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865
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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732
MHB Can You Solve This Week's Challenging System of Equations?
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1
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814
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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874
MHB What Are the Possible Values of c for a Triangle with Area 5?
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1
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734
MHB Can All Outputs of a Quadratic Function Be Integers?
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1
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835
MHB Can Non-zero Polynomials with Real Coefficients Have Real Roots in Common?
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1
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849
MHB Is it possible to find 6-digit numbers with a sum of 8?
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1
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876
MHB Possible Values: $f(8765)-f(4321)$ for Functions Satisfying Inequalities
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1
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770
MHB How Do You Solve POTW #456 for (x+20)(y+20)(z+20)?
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1
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803
MHB Can You Solve the Integer System xz-2yt=3 and xt+yz=1?
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1
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918
MHB What is the Greatest Value of an Expression with Given Numbers and Equation?
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1
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852
MHB Integer Solutions for Equation: POTW #453 - Feb 1st, 2021
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1
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902
MHB Can You Solve This Integer Equation for January 25th, 2021?
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3
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909
MHB How Many Divisors of $30^{2003}$ Are Not Divisors of $20^{2000}$?
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1
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819
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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812
MHB How to Tackle the Latest POTW Inequality Challenge?
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2
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852
MHB Can You Solve for a and b in This Trigonometric Equation?
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1
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761
MHB Triangle with Complex Number Vertices SATISFIES Equilateral Relation
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1
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841
MHB Proof of Regular Heptagon Ratio: AD^3/AB^3 - (AB+2AC)/(AD-AC) = 1
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1
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853
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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835
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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852
MHB Can You Solve the Convex Quadrilateral Angle Mystery?
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2
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969
MHB Can All Roots of This Cubic Equation Be Bounded by 1?
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1
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826
MHB Is the Expression an Integer When Rational Conditions Apply?
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1
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793
MHB Can You Prove These Inequalities for Real Numbers a, b, and c?
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2
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851
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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853
MHB Is It Possible to Prove Real Root Properties in Cubic Equations?
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1
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930
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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872
MHB Quadratic Polynomial Problem: Proving Equality with Real Numbers
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1
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883
MHB Solution to Problem #433: Proving a+b+c=0 yields 9
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1
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842
MHB How Many Final Points Can Be Reached in a Ten-Step Lattice Walk?
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1
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844
MHB How Do Divisors Relate in POTW #431's Integer Equation?
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1
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932
MHB Which Integers Make All Roots of This Polynomial Integer?
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1
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849
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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834
MHB How Can a Fifth Degree Polynomial Meet Specific Divisibility Conditions?
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2
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923
MHB Challenge: Find the Positive Integer for $133^5$ + $110^5$ + $84^5$ + $27^5$
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1
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981
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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902
MHB Can You Solve This Complex Radical Equation?
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1
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869
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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947
MHB How to Calculate the Sum of Squares in Complex Equation Systems?
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1
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892
MHB Problem #422: Four Non-Negative Real Numbers and a Unique Condition
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1
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955
MHB What Natural Numbers Solve the Equation from POTW #421?
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1
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962
MHB Find the Sum of Real Numbers Satisfying Equations
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1
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951
MHB What Is the Probability That a Bridge Is Empty at Noon?
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1
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951
MHB Can you solve this week's POTW: Integrating a Complex Expression? May 25th, 2020
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1
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934
MHB Acute Triangle ABC: Point P and Line Intersections Formula
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1
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828
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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