Question

If a=3-2√2 find the value of (a+1/a)^2

Answer 1

Answer:

$a = 3 - \sqrt[2]{2} \\ {(a + \frac{1}{a} )}^{2} \\ \\ = (3 - \sqrt[2]{2} + { \frac{1}{3 - \sqrt[2]{2} } ) }^{2} \\ \\ = {(3 - \sqrt[2]{2)} }^{2} + { (\frac{1}{3 - \sqrt[2]{2} } )}^{2} + 2 \times (3 - \sqrt[2]{2} ) \times ( \frac{1}{3 - \sqrt[2]{2} } ) \\ \\ =( 9 + 8 - \sqrt[12]{2} ) + \frac{1}{9 + 8 - \sqrt[12]{2} } + 2 \times 1 \\ \\ = 17 - \sqrt[12]{2} + \frac{1}{17 - \sqrt[12]{2}} + 2$