Question

if a^2+1/a^2=11 find a^3-1/a^3​

Answer 1

Step-by-step explanation:

(a-1/a)=3 ( 3)*3-3*3 27-9=18

Answer 2

$a {}^{2} + \frac{1}{a {}^{2} } = 11 \\ = > (a - \frac{1}{a} ) {}^{2} + 2 \times a \times \frac{1}{a} = 11 \\ = > (a - \frac{1}{a} ) {}^{2} = 9 \\ = > (a - \frac{1}{a} ) = \sqrt{9} \\ = > (a - \frac{1}{a} ) = 3$

now...

$a {}^{3} - \frac{1}{a {}^{3} } = (a - \frac{1}{a} )(a {}^{2} + \frac{1}{a {}^{2} } + a \times \frac{1}{a} ) \\ = > (a {}^{3} - \frac{1}{a {}^{3} } ) = 3(11 + 1) = 36$