Question

solve it fastly as answer is 322

Answer 1

HEY DEAR

$if \: x = 9 + \sqrt[4]{5} \\ and \: we \: had \: to \: find \: {x}^{2} + \frac{ {1}^{} }{ {x}^{2} } \\ = \geqslant (9 + \sqrt[4]{5} ) {}^{2} + \frac{1}{(9 + \sqrt[4]{5} } ){}^{2} \\ \\ value \: of \: (\sqrt[4]{5} ) {}^{2} = 80 \: as \: 4 \times 4 = \\ 16 \: and \: \sqrt{5} {}^{2} = 5 \: and \: their \: product \\ \: is \: 80 \\ so \: putting \: valu(81 + 80) + \frac{1}{80 + 81} \\ = \geqslant = \geqslant 61 + \frac{1}{61} \\ = \geqslant \frac{62}{61} \\ thanks.....$

Answer 2

Answer:

x² + 1/x² = 322

Step-by-step explanation:

Given: x = 9 + 4√5

(i)

(1/x) = (1/9 + 4√5) * [(9 - 4√5)/(9 - 4√5)]

      = [(9 - 4√5)/(9²) - (4√5)²]

      = [(9 - 4√5)]

(ii)

x + 1/x = (9 - 4√5) + (9 + 4√5)

          = 18

On squaring both sides, we get

⇒ (x + 1/x)² = (18)²

⇒ x² + 1/x² + 2 = 324

⇒ x² + 1/x² = 322.

Hope it helps!