Question

If $x+\frac{1}{x}=2$, find the value of $x^{64}+\frac{1}{x^{64}}$

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

The correct option is D: $2$

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

Squaring both sides, we get $x^2+\frac{1}{x^2}+2\times x.\times \frac{1}{x}=4$

So, $x^2+\frac{1}{x^2}=4-2=2$

Again Squaring both sides, we get $x^4+\frac{1}{x^4}+2\times x^2\times \frac{1}{x^2}=4$

$\Rightarrow x^4+\frac{1}{x^4}=4-2=2$

Similarly, $x^8+\frac{1}{x^8}=x^{32}+\frac{1}{x^{32}}=x^{64}+\frac{1}{x^{64}}=2$