Question

se x+1/x=3, determine o valor de x^3+1/x^3​

Answer 1

Olá,

$\sf \frac{x + 1}{x} = 3 \\ \sf \: \frac{x}{x} + \frac{1}{x} = 3 \\ \sf \: 1 + \frac{1}{x} = 3 \\ \sf \: \frac{1}{x} = 3 - 1 \\ \sf \: \frac{1}{x} = 2 \\ \sf \: ( \frac{1}{x} {)}^{3} = {2}^{3} \\ \sf \: \frac{1}{ {x}^{3} } = 8 \\ \sf \red{1 + } \frac{1}{ {x}^{3} } = 8 \red{ + 1} \\ \sf \: \frac{ {x}^{3} }{ {x}^{3} } + \frac{1}{ {x}^{3} } = 9 \\ \boxed{ \sf \: \frac{ {x}^{3} + 1 }{ {x}^{3} } = 9 }$