Question

$x- \frac{1}{x}$ = 2, resolva x³-2x² -  $\frac{2}{x^{2} }$ - $\frac{1}{x^{3} }<span>$. 

Answer 1

Oi Styxer

x - 1/x = 2

(x - 1/x)² = x² - 2x/x + 1/x² = 4

x² + 1/x² = 4 + 2 = 6 

2x² + 2/x² = 2*6 = 12

(x - 1/x)³ = x³ - 1/x³ - 3*(x - 1/x) = 8

x³ - 1/x³ = 8 + 3*2 = 14 

x³ - 1/x³ - 2x² - 2/x² = 14 - 12 = 2

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