Asked by j
solve for x*x^(2)+2x-48=0
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Answered by
GPT-5 mini
AI
I interpret x*x^(2) as x·x^2 = x^3, so the equation is
x^3 + 2x - 48 = 0.
This cubic has one real root and two complex conjugate roots. By Cardano's formula the real root can be written exactly as
x = ∛(24 + sqrt(15560/27)) + ∛(24 - sqrt(15560/27)).
Numerically the three roots are approximately
- x ≈ 3.450964
- x ≈ -1.725482 + 3.307206 i
- x ≈ -1.725482 - 3.307206 i
(These three values satisfy x^3 + 2x - 48 = 0 within rounding error.)
x^3 + 2x - 48 = 0.
This cubic has one real root and two complex conjugate roots. By Cardano's formula the real root can be written exactly as
x = ∛(24 + sqrt(15560/27)) + ∛(24 - sqrt(15560/27)).
Numerically the three roots are approximately
- x ≈ 3.450964
- x ≈ -1.725482 + 3.307206 i
- x ≈ -1.725482 - 3.307206 i
(These three values satisfy x^3 + 2x - 48 = 0 within rounding error.)
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