Question

a= 3-2√2 find value of a ²-1/a²​

Answer 1

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

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

${(3 + 2 \sqrt{2)} }^{2} = 9 + 4 \sqrt{2} + 8$

${(3 - 2 \sqrt{2} )}^{2} = 9 - 4 \sqrt{2} + 8$

$9 - 4 \sqrt{2} + 8 - 9 + 4 \sqrt{2} + 8 \\ \\ = 8 + 8 \\ \\ = 16$