Question

$if x+ \frac{1}{x}=10 then, x^{2} + \frac{1}{ x^{2} } =?$

Answer 1

x+1/x=10
squarin on both sides we get
(x+1/x)^2=10^2
x^2+1/(x^2)+2*x*1/x=100
x^2+1/(x^2)+2=100
Adding -2 on both sides
x^2+1/(x^2)+2-2=100-2
x^2+1/(x^2)=98

Answer 2

$a^2+b^2 = (a+b)^2 - 2ab$

$x^2 + \frac{1}{x^2} = (x + \frac{1}{x})^2 - 2*x* \frac{1}{x}$

$x^2 + \frac{1}{x^2} = (10)^2 - 2$

$x^2 + \frac{1}{x^2} = 100-2 = 98$