Question

Doar cei care se pricep! ​

Answer 1

Explicație pas cu pas:

$x + \dfrac{1}{x} = 3$

$\bigg(x + \dfrac{1}{x}\bigg)^{3} = x^3 + 3 \cdot x^{2} \cdot \dfrac{1}{x} + 3 \cdot x \cdot \dfrac{1}{x^{2}} + \dfrac{1}{x^{3}} = \\ = x^3 + 3x + \dfrac{3}{x} + \dfrac{1}{x^{3}} = x^3 + 3\bigg(x + \dfrac{1}{x}\bigg) + \dfrac{1}{x^{3}}$

$3^{3} = x^3 + 3 \cdot 3 + \dfrac{1}{x^{3}}$

$x^3 + \dfrac{1}{x^{3}} = 27 - 9 \implies x^3 + \dfrac{1}{x^{3}} = \bf 18$