Question

If x square + 1 by x square is equals to 38 the value of x minus one by x is​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

SOLUTION :

GIVEN

$\displaystyle \sf{ \: } {x}^{2} + \frac{1}{ {x}^{2} } = 38$

TO DETERMINE

$\displaystyle \sf{ \: }x - \frac{1}{x}$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$\sf{} {a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab$

CALCULATION

It is given that

$\displaystyle \sf{ \: } {x}^{2} + \frac{1}{ {x}^{2} } = 38$

$\implies\displaystyle \sf{} { \bigg(x - \frac{1}{x} \bigg) }^{2} + 2.x. \frac{1}{x} = 38$ ( Using above identity )

$\implies\displaystyle \sf{} { \bigg(x - \frac{1}{x} \bigg) }^{2} + 2 = 38$

$\implies\displaystyle \sf{} { \bigg(x - \frac{1}{x} \bigg) }^{2} = 36$

$\implies\displaystyle \sf{} { \bigg(x - \frac{1}{x} \bigg) } = \pm \: 6$

FINAL RESULT

$\boxed{\displaystyle \sf{} \: { \bigg(x - \frac{1}{x} \bigg) } = \pm \: 6 \: \: }$

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