Question

If $x^{50}+\frac{1}{x^{50}}=2$ then $x^{100}+\frac{1}{x^{100}}=$?

Answer 1

Given $x^{50}+\frac{1}{x^{50}}=2$

$x^{100}+\frac{1}{x^{100}}=x^{100}+\frac{1}{x^{100}}+2x^{50}\frac{1}{x^{50}}-2x^{50}\frac{1}{x^{50}}$

$={(x^{50}+\frac{1}{x^{50}})}^2-2$

$=2^2-2$

$=4-2$

$=2$