# If x + (1/x) = 2 then x2 + (1/x2​) = ?

Answer: $x^{2}+ \frac{1}{x^{2}} = 2$

Given

$x + \frac{1}{x}= 2$

To find:

$x^{2} + \frac{1}{x^{2}}$

Squaring on both the side we get

$\left (x + \frac{1}{x} \right)^{2}= 2^{2}$ $\left (x + \frac{1}{x} \right)^{2}= 4$ $x^{2}+ \frac{1}{x^{2}}+ 2\times x\times \frac{1}{x}= 4$ $x^{2}+ \frac{1}{x^{2}}+ 2 = 4$ $x^{2}+ \frac{1}{x^{2}} = 4 – 2$ $x^{2}+ \frac{1}{x^{2}} = 2$