Question

Is this is right???......

Answer 1

Hello Mate!

In your solution I think,

Till the line I drawn is correct, further solution in continuation I am doing.

$x = \sqrt{5} + 2 \\ {x}^{2} = {( \sqrt{5} + 2)}^{2} \\ { \sqrt{5} }^{2} + {2}^{2} + 2 \times 2 \times \sqrt{5} \\ 5 + 4 + 4 \sqrt{5} = 9 + 4 \sqrt{5} \\ \frac{1}{ {x}^{2} } = \frac{1}{9 + 4 \sqrt{5} } \times \frac{9 - 4 \sqrt{5} }{9 - 4 \sqrt{5} } \\ \frac{9 - 4 \sqrt{5} }{81 - (16 \times 5)} = 9 - 4 \sqrt{5} \\ {x}^{2} - \frac{1}{ {x}^{2} } = 9 + 4 \sqrt{5} - (9 - 4 \sqrt{5} ) \\ 9 + 4 \sqrt{5} - 9 + 4 \sqrt{5} \\ 8 \sqrt{5}$


Hope this time u will understand it frnd.