Question

si
$x + \frac{1}{x} = 4$
calcular
$x ^{3} + \frac{1}{ {x}^{3} }$
​

Answer 1

Se desarrolla la expresión (x + 1/x)³ = x³ + 3 x² . 1/x + 3 x (1/x)² + 1/x³

4³ = x³ + 1/x³ + 3 (x + 1/x) = 3 . 4 = 12

O sea x³+ 1/x³= 64 - 12 = 52

Mateo