Question

a+1/a=10 and2square -1/a square slove

Answer 1

a+ 1/a =10 ----------------------------(1)
(a+1/a)^2 =100
a^2 +(1/a)^2 +2*a*1/a =100
a^2 +(1/a)^2 +2 = 100
a^2 +(1/a)^2 = 98------------------(2)

Now,
(a-1/a)^2 = a^2 + (1/a)^2 - 2*a*1/a
(a-1/a)^2 = 98 - 2 (Using equation 2)

$a - \frac{1}{a} = \sqrt{96}$
$a - \frac{1}{a} = 2 \sqrt{14}$
Now,

${a}^{2} - { (\frac{1}{a}) }^{2} = (a + \frac{1}{a} )(a - \frac{1}{a} )$

a^2 - (1/a) ^2 = (10)(2 root 14)

${a}^{2} - \frac{1}{ {a}^{2} } = 20 \sqrt{14}$