Question

If a +1/a= 6 and a≠ 0; find :(i). a-1/a (ii). a^2-a-1/a^2


plz answer it fast​

Answer 1

$Given \: a + \frac{1}{a} = 6 \: ---(1)$

$i ) \Big( a - \frac{1}{a} \Big)^{2}\\ = \Big( a + \frac{1}{a} \Big)^{2} -2 \\= 6^{2} - 4 \: [ From \:(1) ] \\= 36 - 4 \\= 32$

$ii ) \Big( a - \frac{1}{a} \Big)\\= \sqrt{32} \\= 4\sqrt{2} \: --(2)$

$iii ) a^{2} - \frac{1}{a^{2}} \\= \Big( a + \frac{1}{a} \Big) \Big( a - \frac{1}{a} \Big) \\= 6 \times 4\sqrt{2} \\= 24\sqrt{2}$

•••♪