How to solve this inequality involving a 4th root?

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In summary, the conversation discusses a problem with solving an inequality involving a 4th root term and a binomial. The suggested solution is to expand the 4th root as a binomial or Taylor series and solve the inequalities separately. The final solution is -0.368935 < x < 0.677669.
  • #1
PhizKid
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Homework Statement


[tex]\sqrt[4]{2x + 1} - 0.1 < \frac{1}{2}x + 1 < \sqrt[4]{2x + 1} + 0.1[/tex]


Homework Equations





The Attempt at a Solution



I'm having trouble getting just an 'x' by itself in the middle because of the 4th root. How should I solve this inequality? I tried everything but always end up with something to the 4th power after expanding 4 binomials.

(Solution: -0.368935 < x < 0.677669)
 
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  • #2
PhizKid said:

Homework Statement


[tex]\sqrt[4]{2x + 1} - 0.1 < \frac{1}{2}x + 1 < \sqrt[4]{2x + 1} + 0.1[/tex]

I'm having trouble getting just an 'x' by itself in the middle because of the 4th root. How should I solve this inequality? I tried everything but always end up with something to the 4th power after expanding 4 binomials.

(Solution: -0.368935 < x < 0.677669)

I would think about expanding ##\sqrt[4]{1+2x}## as a binomial or Taylor series with error estimates.
 
  • #3
Try to solve the inequalities separately.

[tex]\sqrt[4]{2x + 1} < \frac{1}{2}x + 1.1 [/tex]
[tex]\sqrt[4]{2x + 1} > \frac{1}{2}x + 0.9 [/tex]

ehild
 

Related to How to solve this inequality involving a 4th root?

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