Question

1Resolva a Eq. 8x⁶ + 7x³ - 1 = 0​

Answer 1

Resposta:

S = {-1, 1/2}

Explicação passo a passo:

8x⁶ + 7x³ - 1 = 0​

Resolvendo no conjunto dos Reais.

Seja x³ = y

8(x³)² + 7x³ - 1 = 0

8y² + 7y - 1 = 0

$\Delta =7^2-4.8(-1)\\\\\Delta=49+32\\\\\Delta= 81\\\\y=\frac{-b\pm\sqrt{\Delta} }{2a} \\\\y=\frac{-7\pm9}{2.8}\\\\y=\frac{-16}{16} }=-1\\\\y=\frac{2}{16}=\frac{1}{8} \\\\\\x^3=-1\implies x=\sqrt[3]{-1} \implies x=-1\\\\x^3=\frac{1}{8}\implies x=\sqrt[3]{\frac{1}{8} } \implies x=\frac{1}{2}$