Question

If
$x {}^{2} + \frac{1}{ {x}^{2} } = 7$
then find the value of
$x {}^{3} + \frac{1}{ {x}^{3} }$

Answer 1

(x+1/x)^2=x^2+1/x^2+2x×1/x
(x+1/x^2)=7+2=9
x+1/x=3
again
(x^3+1/x^3)=(x+1/x)(x^2+1/x^2-x×1/x)
=3×(7-1)=3×6=18
is your answer