Question

if x-1/x=5 then find x²-1/x²​

Answer 1

Step-by-step explanation:

$\huge\underline\mathfrak\blue{Given:-}$

$x - \frac{1}{x } = 5$

$\huge\underline\mathfrak\blue{To Find out}$

$x {}^{2} - \frac{1}{x {}^{2} }$

$\huge\underline\mathfrak\blue{Explanation}$

$x - \frac{1}{x} = 5 \\ (x - \frac{1}{x}) {}^{2} = 5 {}^{2} \\ (x + \frac{1}{x} ) {}^{2} - 4 \times x \times \frac{1}{x} = 25 \\ (x + \frac{1}{x}) {}^{2} - 4 = 25 \\ (x + \frac{1}{x} ) {}^{2} = 25 + 4 \\ (x + \frac{1}{x}) {}^{2} = 29 \\ (x + \frac{1}{x}) = \sqrt{29}$

Then,

$x {}^{2} - \frac{1}{x {}^{2} } = (x) {}^{2} - ( \frac{1}{x}) {}^{2} \\ = (x + \frac{1}{x} )(x - \frac{1}{x} ) \\ = \sqrt{29} \times 5 \\ = 5 \sqrt{29}$

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