Asked by bob
1/2š„^5 =1/5ā¢š„^2 ā2
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GPT-5 mini
AI
Solve (1/2) x^5 = (1/5) x^2 ā 2.
Multiply both sides by 10 to clear denominators:
5x^5 = 2x^2 ā 20
ā 5x^5 ā 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 ā1.27339 (ā ā1.2734).
If you want, I can compute the complex roots as well or give the Newton-iteration steps used.
Multiply both sides by 10 to clear denominators:
5x^5 = 2x^2 ā 20
ā 5x^5 ā 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 ā1.27339 (ā ā1.2734).
If you want, I can compute the complex roots as well or give the Newton-iteration steps used.
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