Question

Se x + 1/x = 3/5, qual o valor de x³ + 1/x³ ?

Answer 1

Resposta:

$-\frac{273}{250}$

Explicação passo a passo:

$x + \frac{1}{x}=\frac{3}{5} ~~(Quadrando)\\\\x^2+2x*\frac{1}{x}+\frac{1}{x^2}=\frac{9}{25}\\\\x^2+\frac{1}{x^2}=\frac{9}{25}-2\\\\x^2+\frac{1}{x^2}=-\frac{41}{50} \\\\x^3+\frac{1}{x^3}=(x+\frac{1}{x})(x^2-x*\frac{1}{x}+\frac{1}{x^2} )=\\\\ (x+\frac{1}{x})(x^2+\frac{1}{x^2} -1)= \frac{3}{5} (-\frac{41}{50}-1)=\frac{3}{5}(-\frac{91}{50}) = -\frac{273}{250}$