if x+1/x =2 then x16+1/x16 is equal to gives answer

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Solution

$x + \frac{1}{x} = 2 \Rightarrow {(x + \frac{1}{x})}^{2} = 2^{2} {on squaring both sides} \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 4 \Rightarrow x^{2} + \frac{1}{x^{2}} = 2 \Rightarrow {(x^{2} + \frac{1}{x^{2}})}^{2} = 4 {On squaring both sides} \Rightarrow x^{4} + \frac{1}{x^{4}} + 2 = 4 \Rightarrow x^{4} + \frac{1}{x^{4}} = 2 \Rightarrow {(x^{4} + \frac{1}{x^{4}})}^{2} = 4 {on squaring both sides} \Rightarrow x^{8} + \frac{1}{x^{8}} + 2 = 4 \Rightarrow x^{8} + \frac{1}{x^{8}} = 2 \Rightarrow {(x^{8} + \frac{1}{x^{8}})}^{2} = 4 {on squaring both sides} \Rightarrow x^{16} + \frac{1}{x^{16}} + 2 = 4 \Rightarrow x^{16} + \frac{1}{x^{16}} = 2$

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