Question

please solve the fast important

Answer 1

$Given : \frac{\sqrt{5} + 1}{\sqrt{5} - 1} +\frac{\sqrt{5} - 1 }{\sqrt{5} + 1}$

$=> \frac{(\sqrt{5} + 1)(\sqrt{5} + 1) + (\sqrt{5} - 1)(\sqrt{5} - 1)}{(\sqrt{5} - 1)(\sqrt{5} + 1)}$

$=> \frac{(\sqrt{5} + 1)^2 + (\sqrt{5} - 1)^2}{(\sqrt{5})^2 - (1)^2 }$

$=> \frac{(\sqrt{5} + 1)^2 + (\sqrt{5} - 1)^2}{5 - 1}$

$=> \frac{(\sqrt{5} + 1)^2 + (\sqrt{5} - 1)^2}{4}$

$=> \frac{(5 + 2\sqrt{5} + 1) + (5 - 2\sqrt{5} + 1)}{4}$

$=> \frac{5 + 2\sqrt{5} + 1 + 5 - 2\sqrt{5} + 1}{4}$

$=> \frac{12}{4}$

$=> 3$

Now,

$=> 3 = a + b\sqrt{5}$

It can be written as,

$=> 3 + 0\sqrt{5} = a + b\sqrt{5}$

Therefore:

The value of a = 3 and b = 0.

Hope this helps!

Answer 2

hey!
the answer is,
a = 3, b = 0