Question

If a = 3- 2√2 . Find the value of a^2 - 1 / a^2​

Answer 1

Answer:

$a = 3 - 2 \sqrt{2}$

$\frac{1}{a} = \frac{1}{3 - 2 \sqrt{2} }$

$\frac{1}{a} = \frac{3 + 2 \sqrt{2} }{9 - 8}$

$\frac{1}{a} = 3 + 2 \sqrt{2}$

$a + \frac{1}{a} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2}$

$a + \frac{1}{a} = 6$

$a - \frac{1}{a} = - 4 \sqrt{2}$

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

=

$6 \times - 4 \sqrt{2} = - 24 \sqrt{2}$

Answer 2

So this is your required answer.