Solve x^2+7x>6+2x^3: Tips & Solutions

  • Context: Undergrad 
  • Thread starter Thread starter Gughanath
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Discussion Overview

The discussion revolves around solving the inequality x^2 + 7x > 6 + 2x^3. Participants are exploring various approaches to manipulate and solve the inequality, with a focus on algebraic techniques and factorization.

Discussion Character

  • Homework-related, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant expresses difficulty in solving the inequality and requests help.
  • Another participant reformulates the inequality into a polynomial equation, suggesting to solve -2x^3 + x^2 + 7x - 6 = 0.
  • A similar reformulation is repeated by another participant, who also admits to struggling with the solution.
  • One participant proposes that since the sum of the coefficients is 1, (x-1) is a factor, providing a factorization of the polynomial as (x-1)(x+2)(2x-3).
  • Another participant suggests a different approach by rearranging the inequality to 2x^3 - x^2 - x < 0 and discusses implications regarding the signs of the factors.
  • This latter approach is reiterated, emphasizing that either x < 0 or (2x^2 - x - 1) < 0 must hold for the expression to be negative.
  • One participant points out a potential misunderstanding in the problem statement, asserting that the correct form should be x^2 + 7x > 6 + 2x^3.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to solve the inequality, and multiple competing views and methods are presented without resolution.

Contextual Notes

Some participants express uncertainty in their methods, and there are differing interpretations of the problem statement, which may affect the approaches taken.

Gughanath
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x^2+7x>6+2x^3...I tried many times..i can't solve this ...please help
 
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x^2 + 7x > 6 + 2x^3 = -2x^3 + x^2 + 7x - 6 > 0

Try solving for:
-2x^3 + x^2 + 7x - 6 = 0
 
Dr-NiKoN said:
x^2 + 7x > 6 + 2x^3 = -2x^3 + x^2 + 7x - 6 > 0

Try solving for:
-2x^3 + x^2 + 7x - 6 = 0

I can't solve that sorry...could you help any further?
 
I noticed the sum of the coefficients is 1 so (x-1) is a factor:

[tex]2x^3-x^2-7x+6 = (x-1)(x+2)(2x-3)[/tex]

That should get you started!
 
try it,
x^2 + 7x>6x + 2x^3
or, 2x^3 - x^2 -x<0
or, x(2x^2 - x - 1)<0
this implies, either x<0 or (2x^2 - x - 1) <0
as the expression is negative which is only possible if one of the term is negative.
 
aekanshchumber said:
try it,
x^2 + 7x>6x + 2x^3
or, 2x^3 - x^2 -x<0
or, x(2x^2 - x - 1)<0
this implies, either x<0 or (2x^2 - x - 1) <0
as the expression is negative which is only possible if one of the term is negative.
You have read the problem incorrectly. It should read
[tex]x^2 + 7x > 6 + 2x^3[/tex]
 
Last edited:

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