Question

if a-1/a =2 than a^2-1/a^2=?​

Answer 1

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

${a}^{2} + \frac{1}{ {a}^{2} } - 2 = 4$

${a}^{2} + \frac{1}{ {a}^{2} } = 6....(i)$

Now,

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

From (I)

${(a + \frac{1}{a}) }^{2} = 6 + 2$

${(a + \frac{1}{a}) }^{2} = 8$

$a + \frac{1}{a} = 2 \sqrt{2}$

As,

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

Now put the values

$= 2 \sqrt{2} \times 2$

$= 4 \sqrt{2}$