Question

if x^3+1/x^3=2 find x+1/x

Answer 1

Answer:

${(x + \frac{1}{x}) }^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} ) \\ \\ suppose \: \: that \: \: x + \frac{1}{x} = t \\ \\ {t}^{3} = 2 + 3t \\ \\ t = 2 \: \: \: and \: \: t = - 1 \\ \\ x + \frac{1}{x} = 2 \\ x = 2 \\ \\ \\ x + \frac{1}{x} = - 1 \\ {x}^{2} + x + 1 = 0(no \: solution) \\ \\ \\ \\ x = 2$