Question

x^2+1/x^2=7, find x-1/x​

Answer 1

Answer:

√5

Step-by-step explanation:

$x^2 + \dfrac{1}{x^2} = 7\\\\\\\text{Taking \left( x - \dfrac{1}{x} \right)^2 , we have}\\\\\\\left( x - \dfrac{1}{x} \right)^2 = x^2 + \dfrac{1}{x^2} - 2(x) \left( \dfrac{1}{x} \right)\\\\\\\implies x - \dfrac{1}{x} = \pm \: \sqrt{7 - 2}\\\\\\= \boxed{\pm \: \sqrt{5}}$

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } = 7 \\ \\ \\{x}^{2} + \frac{1}{ {x}^{2} } - 2 = 7 - 2 \\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2.x.\frac{1}{x} = 7 - 2 \\ \\ \\ {(x - \frac{1}{x})}^{2} = 5 \\ \\ \\x - \frac{1}{x} = \pm \sqrt{5}$

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Therefore :-

$\boxed{\bold{x- \frac{1}{x}= \pm \sqrt{5}}}$

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Things used :-

1)Identities :-

$(x- \dfrac{1}{x})^{2}= x^{2}+ \dfrac{1}{x^{2}} - 2.x. \frac{1}{x}$

2)Solving linear equations and transposing of square into square Root on opposite side.

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