Question

someone please answer this​

Answer 1

Answer:

I think the answer is - 72 root 5

Step-by-step explanation:

once check the solution which is provided in the picture pinned to this answer.

Hope this helps you

Answer 2

Answer:

Given,

$x = \frac{2 + \sqrt{5} }{2 - \sqrt{5} }$

By Rationalisation of denominator,

we get,

$\frac{2 + \sqrt{5} }{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} }$

$= \frac{( {2})^{2} +2 \times 2 \times \sqrt{5} + ( \sqrt{5} )^{2}}{(2) {}^{2} - (\sqrt{5}) {}^{2} }$

$= \frac{4 + 2 \sqrt{5} + 5 }{4 - 5}$

$= \frac{9 + 2 \sqrt{5} }{ - 1}$

$= - 9 - 2 \sqrt{5}$

Now,

$y = \frac{2 - \sqrt{5} }{2 + \sqrt{5} }$

$\frac{2 - \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} }$

$= \frac{( {2})^{2} - 2 \times 2 \times \sqrt{5} + ( \sqrt{5} )^{2}}{(2) {}^{2} - (\sqrt{5}) {}^{2} }$

$= \frac{4 - 2 \sqrt{5} + 5 }{4 - 5}$

$= \frac{9 - 2 \sqrt{5} }{ - 1}$

$= - 9 + 2 \sqrt{5}$

$now \\ x {}^{2} - y {}^{2}$

$= ( - 9 - 2 \sqrt{5} ) {}^{2} - ( - 9 + 2 \sqrt{5} ) {}^{2}$

$= (81 + 4 \times 5) - (81 + 4 \times 5)$

$= 81 - 81 - 20 - 20 \\ = 0$

THEREFORE,

$x {}^{2} - y {}^{2} = 0$