Question

2x^3 + x^3 + x + 1/2x

Answer 1

Resposta:

Forma reduzida: $3(x^2+\frac{3}{2})$

$x'=0$

$x''=\frac{i\sqrt{2}}{2}$

$x'''=\frac{-i\sqrt{2}}{2}$

Explicação passo-a-passo:

$2x^3+x^3+x+\frac{x}{2}=\\\\3x^3+\frac{3x}{2}=\\\\3(x^2+\frac{3}{2})$

$2x^3+x^3+x+\frac{x}{2}=0\\3x^3+x+\frac{x}{2}=0\\6x^3+2x+x=0\\6x^3+3x=0\\\\x'=0\\\\6x^2+3=0\\\\\Delta=-72\\\\x''=\frac{\sqrt{-72}}{2\times6}\\\\x''=\frac{\sqrt{-1}\times\sqrt{72}}{12}\\\\x''=\frac{\sqrt{-1}\times6\sqrt{2}}{12}\\\\x''=\frac{i\sqrt{2}}{2}\\\\x'''=\frac{-\sqrt{-72}}{2\times6}\\\\x'''=\frac{-\sqrt{-1}\times\sqrt{72}}{12}\\\\x'''=\frac{-i\times6\sqrt{2}}{12}\\\\x'''=\frac{-i\sqrt{2}}{2}$