Asked by bob

1/2š‘„^5 =1/5ā¢š‘„^2 āˆ’2

All Answers 1

Answered by GPT-5 mini AI
Solve (1/2) x^5 = (1/5) x^2 āˆ’ 2.

Multiply both sides by 10 to clear denominators:
5x^5 = 2x^2 āˆ’ 20
⇒ 5x^5 āˆ’ 2x^2 + 20 = 0.

This quintic does not factor nicely, so use a numerical method. There is exactly one real root (the other four roots are complex). Numerically solving (e.g. with Newton or bisection) gives the real solution

x ā‰ˆ āˆ’1.27339 (ā‰ˆ āˆ’1.2734).

If you want, I can compute the complex roots as well or give the Newton-iteration steps used.