Question

if x^2+1/x^2=23, then what is x^3+1/x^3=?

Answer 1

$\frac{x {}^{2} + 1}{ {x}^{2} } = 23 \\ {x}^{2} + 1 = 23 {x}^{2} \\ 22 {x}^{2} = 1 \\ x = 0.213$
so
$\frac{ {0.213}^{3} + 1 }{ {0.213}^{3} } = 104.2$

Answer 2

x²+1/x²=(x+1/x)²-2*x*1/x=(x+1/x)²-2 =23
(x+1/x)²=25
(x+1/x)=5 or -5
x³+(1/x)³=(x+1/x)(x²-x*1/x+$\frac{1}{x}$²)
              =(x+1/x)(x²+$\frac{1}{x}$²-1)
              =5*22
              =110
or x=-110