Question

Avem $x +\frac{1}{x} =4 Determinati x^ {3} + \frac{1}{x^ {3}}$

Answer 1

$x + \frac{1}{x} = 4$ ridicam totul la a3a

$(x + \frac{1}{x})^{3} = 4^{3}$

folosim formula (a+b)³= a³ + 3a²b + 3ab² + b³

$x^{3} + 3 x^{2} \frac{1}{x} + 3x \frac{1}{ x^{2} } + \frac{1}{ x^{3} } = 64$

$x^{3} + 3 x+ \frac{3}{x} + \frac{1}{ x^{3} } = 64$

$x^{3} + 3(x+ \frac{1}{x}) + \frac{1}{ x^{3} } = 64$

$x^{3} + 3* 4 + \frac{1}{ x^{3} } = 64$

$x^{3} + 12 + \frac{1}{ x^{3} } = 64$

$x^{3} + \frac{1}{ x^{3} } = 64 -12$

$x^{3} + \frac{1}{ x^{3} } = 52$