If x+1/x =20, find the value of x^2+1/x^4.

Question

If \(x+\frac{1}{x}\) =20, find the value of \(x^2+\frac{1}{x^4}\).

Answer 1

Given that,

\(x+\frac{1}{x}\) = 20

Squaring both sides, we get

\((x+\frac{1}{x})^2\)= (20)²

x² + 2 × x × \(\frac{1}{x}+(\frac{1}{x})^2\) = 400

x² + 2 + \(\frac{1}{x\times x}\) = 400

x² + \(\frac{1}{x\times x}\) = 398