How to solve for x? (2/9)x^2 + (4/3)x > 0.5^x

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Discussion Overview

The discussion centers on solving the inequality (2/9)x² + (4/3)x > 0.5^x, specifically identifying where the quadratic function exceeds the exponential function. Participants explore methods of solution, including algebraic and numerical approaches.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant expresses difficulty in proving that the solution is where x > 0 and seeks assistance.
  • Another participant suggests that plotting the functions reveals they intersect near x = 1/2, contradicting the initial assumption of x > 0.
  • A numerical analysis indicates the intersection point is approximately 0.4, but questions remain about the feasibility of an algebraic solution.
  • It is noted that solving the inequality algebraically in terms of "usual functions" may not be possible, prompting curiosity about any "unusual" functions that could be used.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the algebraic solvability of the inequality, with some asserting it cannot be solved using standard functions while others remain curious about alternative methods.

Contextual Notes

There is uncertainty regarding the exact intersection point of the functions and the limitations of algebraic methods in this context.

Superposed_Cat
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Hi all, for what I'm currently doing I need to find where that parabola is greater than the exponential equation.This may seem simple but I can't seem to do anything other than rephrase it without getting a solution. Any help appreciated. it seems as though the answer is where x>0 but I can't prove it algebraicly.
 
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Superposed_Cat said:
Hi all, for what I'm currently doing I need to find where that parabola is greater than the exponential equation.This may seem simple but I can't seem to do anything other than rephrase it without getting a solution. Any help appreciated. it seems as though the answer is where x>0 but I can't prove it algebraicly.
With over 300 posts, you should know by now not to put your equations in the title.

If you plot the functions on the two sides of the inequality you will see they cross near ##x=1/2##, not near ##x=0##. You can solve for it numerically.
 
Numerical analysis gives about 0.4, you are right. But is it undoable algebraicaly?
 
Superposed_Cat said:
Numerical analysis gives about 0.4, you are right. But is it undoable algebraicaly?

It is closer to .5 than .4. Yes, you can not solve it algebraically in terms of the usual functions.
 
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Thank you, like your signature by the way. "usual functions" is there an unusual one to do this job?
 

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