Question

Знадйть x^3+(8/x^3), якщо x+(2/x)=4

Answer 1

Ответ:

40

Объяснение:

$\displaystyle\\x^3+\frac{8}{x^3}=\bigg(x+\frac{2}{x}\bigg )^3- 3x^2\cdot\frac{2}{x} -3x\cdot\bigg(\frac{2}{x}\bigg)^2 =\\\\\\=\bigg(x+\frac{2}{x}\bigg )^3-6x-\frac{12}{x}=\bigg(x+\frac{2}{x}\bigg )^3 -6\bigg(x+\frac{2}{x}\bigg) =\\\\\\=4^3-6*4=64-24=40$