Question

If a-1/a =-6, find the value of a²+1/a².


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Answer 1

Step-by-step explanation:

I think it may help you, we just have to do square both sides using identity (a-b)^2=a^2+b^2-2ab

Answer 2

Question:-

$\: \bf \:if \: \: a - \frac{1}{a} = - 6 \: \: find \: value \: of \: {a}^{2} + \frac{1}{ {a}^{2} }$

Solution:-

we have

$\bf \: a - \frac{1}{a} \: = \: - 6$

Squaring on both side we get

$( \bf \: a - \frac{1}{a} ) {}^{2} = ( - 6) {}^{2}$

Use this identity => (a - b ) ² = a² + b² - 2ab

$\bf \: {a}^{2} + \frac{1}{ {a}^{2} } - 2 \times a \times \frac{1}{a} = 36$

$\bf \: {a}^{2} + \frac{1}{ {a}^{2} } - 2 \times { \not \:a }\times \frac{1}{ \not \: a} = 36$

$\bf \: {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 36$

$\bf \: {a}^{2} + \frac{1}{ {a}^{2} } = 36 + 2$

$\bf \: {a}^{2} + \frac{1}{ {a}^{2} } = 38$

So value of a² + 1 / a² = 38