Question

Please answer this question fast....
If a^2+9/a^2=31, what will be the value of a-3/a

Answer 1

ANSWER:

Given:

If a² +9/a² =31

To find:

a-3/a

Explanation:

Using Identity of (a-b)²= a² +b² -2ab

$(a - \frac{3}{a}) {}^{2} = ( {a)}^{2} + ( { \frac{3}{a}) }^{2} - 2 \times \: a \times \frac{3}{a} \\ \\ = > ( {a}- \frac{3}{a} ) {}^{2} = {a}^{2} + \frac{9}{ {a}^{2} } - 6 \\ \\ = > (a - \frac{3}{a }) {}^{2} = 31 - 6 \\ \\ = > ( a + \frac{3}{a} ) {}^{2} = 25 \\ \\ = > (a + \frac{3}{a} ) = \sqrt{25} \\ \\ = > a + \frac{3}{a} = 5$

Thus,

The value is 5.

Thank you.