Question

If a² +(9 / a²) =31 then a -(3 /a) is equal to

5

40

20

​

Answer 1

$Given \: a^{2} + \frac{9}{a^{2}} = 31$

$\implies a^{2} + \Big(\frac{3}{a}\Big)^{2} = 31$

$\implies a^{2} + \Big(\frac{3}{a}\Big)^{2} - 2 \times a \times \frac{3}{a} = 31 - 2 \times a \times \frac{3}{a}$

/* By Algebraic identity */

$\boxed{\pink{ x^{2} + y^{2} - 2xy = (x-y)^{2} }}$

$\implies \Big( a - \frac{3}{a}\Big)^{2} = 31 - 2 \times 3$

$\implies \Big( a - \frac{3}{a}\Big)^{2} = 31 - 6$

$\implies \Big( a - \frac{3}{a}\Big)^{2} =25$

$\implies a - \frac{3}{a}=\pm \sqrt{25 }$

$\implies a - \frac{3}{a}=\pm 5$

Therefore.,

$\red{Value \:of \: a - \frac{3}{a}}=\pm 5 }$

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