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

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

Answer»

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

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