If \(x+\frac{1}{x}=12\) find the value of \(x-\frac{1}{x}\).

1.	If \(x+\frac{1}{x}=12\) find the value of \(x-\frac{1}{x}\).
Answer» Given that, x + \(\frac{1}{x}\) = 12 Squaring both sides, we get (x + \(\frac{1}{x}\) )² = 12² x² + (\(\frac{1}{x}\))² + 2 × x × \(\frac{1}{x}\) = 144 x² + \(\frac{1}{x^2}\) = 142 Subtract 2 from both sides, we get x² + \(\frac{1}{x\times x}\) - 2 × x × \(\frac{1}{x}\) = 142 – 2 (x - \(\frac{1}{x}\))² = 140 x - \(\frac{1}{x}\) = \(\sqrt{140}\)

Answer»

Given that,

x + \(\frac{1}{x}\) = 12

Squaring both sides, we get

(x + \(\frac{1}{x}\) )² = 12²

x² + (\(\frac{1}{x}\))² + 2 × x × \(\frac{1}{x}\) = 144

x² + \(\frac{1}{x^2}\) = 142

Subtract 2 from both sides, we get

x² + \(\frac{1}{x\times x}\) - 2 × x × \(\frac{1}{x}\) = 142 – 2

(x - \(\frac{1}{x}\))² = 140

x - \(\frac{1}{x}\) = \(\sqrt{140}\)

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