If \(x+\frac{1}{x} = 9\) find the value of \(x^4+\frac{1}{x^4}\)

1.	If \(x+\frac{1}{x} = 9\) find the value of \(x^4+\frac{1}{x^4}\)
Answer» Given that, x + \(\frac{1}{x}\) = 9 Squaring both sides, we get (x + \(\frac{1}{x}\))² = 9² x² + \(\frac{1}{x\times x}\) + 2 = 81 x² + \(\frac{1}{x\times x}\) = 79 Again, Squaring both sides, we get (x² + \(\frac{1}{x\times x}\) )² = 79² x⁴ + \(\frac{1}{x\times x\times x\times x}\) + 2 = 6241 x⁴ + \(\frac{1}{x\times x\times x\times x}\) = 6239

Answer»

Given that, x + \(\frac{1}{x}\) = 9

Squaring both sides, we get

(x + \(\frac{1}{x}\))² = 9²

x² + \(\frac{1}{x\times x}\) + 2 = 81

x² + \(\frac{1}{x\times x}\) = 79

Again,

Squaring both sides, we get

(x² + \(\frac{1}{x\times x}\) )² = 79²

x⁴ + \(\frac{1}{x\times x\times x\times x}\) + 2 = 6241

x⁴ + \(\frac{1}{x\times x\times x\times x}\) = 6239

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