Question

please tell me fast
And please explain it also


And please don't give wrong Answer ​

Answer 1

Answer:

$x=\frac{2+\sqrt{5} }{2-\sqrt{5} } \\\\x=\frac{(2+\sqrt{5}) (2+\sqrt{5} )}{(2-\sqrt{5} )(2+\sqrt{5} )} \\\\x=\frac{(2+\sqrt{5})^{2}}{(4-5)}\\\\x=-(2+\sqrt{5})^{2}$

$y=\frac{2-\sqrt{5} }{2+\sqrt{5} }\\\\y=\frac{(2-\sqrt{5}) (2-\sqrt{5})}{(2+\sqrt{5} )(2-\sqrt{5})}\\\\y=\frac{(2-\sqrt{5})^{2} }{4-5 }\\\\y=-(2-\sqrt{5})^{2}$

$x^{2} -y^{2}\\\\ = [(2+\sqrt{5} )^{4} - [(2-\sqrt{5} )^{4}\\\\=[(2+\sqrt{5} )^{2} +(2-\sqrt{5} )^{2}][(2+\sqrt{5} )^{2} -(2-\sqrt{5} )^{2}]\\\\=[4+4\sqrt{5}+5+4-4\sqrt{5}+5] \ [\ [(2+\sqrt{5} )+(2-\sqrt{5} )][(2+\sqrt{5} )-(2-\sqrt{5} )]\\\\=18[4(2\sqrt{5})] \\\\=144\sqrt{5}$