Question

HELLO MATES...... PLZ HELP....

Answer 1

Answer:

$\boxed{144\sqrt{5}}$

Step-by-step explanation:

$\textsf{Given :}$

$a=\frac{2+\sqrt{5}}{2-\sqrt{5}}\\\implies\frac{2+\sqrt{5}}{2-\sqrt{5}}\times\frac{2+\sqrt{5}}{2+\sqrt{5}}\\\implies \frac{(2+\sqrt{5})^2}{2^2-(\sqrt{5})^2}\\\implies \frac{4+5+4\sqrt{5}}{4-5}\\\implies \frac{9+4\sqrt{5}}{-1}\\\implies -9-4\sqrt{5}$

$\textsf{Also :}$

$b=\frac{2-\sqrt{5}}{2+\sqrt{5}}\\\implies b=\frac{2-\sqrt{5}}{2+\sqrt{5}}\times\frac{2-\sqrt{5}}{2-\sqrt{5}}\\\implies b=\frac{(2-\sqrt{5})^2}{2^2-(\sqrt{5})^2}\\\implies b=\frac{4+5-4\sqrt{5}}{4-5}\\\implies b=\frac{9-4\sqrt{5}}{-1}\\\implies b=4\sqrt{5}-9$

$\textsf{Lets find the given value :}$

$a^2-b^2\\\implies(a+b)(a-b)\\\implies (-9-4\sqrt{5}+4\sqrt{5}-9)(-9-4\sqrt{5}-4\sqrt{5}+9)\\\implies (-18)\times (-8\sqrt{5})\\\implies 144\sqrt{5}$

Answer 2

heya meta...here is ur explanation.


first of all u have to rationalise and simplify the value of a and b.

then u can do easily the calculation.

further see the attachment.

hope it helps U ✌️✌️