Question

Find the value of a and b of a+root5 is (root5+root3)(root5-root3)​

Answer 1

Given:

Consider the value of $a+b\sqrt{5}$ is $(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})$.

To find:

The values of a and b.

Solution:

According to the given information,

$a+b\sqrt{5}=(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})$

$a+b\sqrt{5}=(\sqrt{5})^2-(\sqrt{3})^2$            $[\because a^2-b^2=(a-b)(a+b)]$

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

$a+b\sqrt{5}=2$

It can be written as

$a+b\sqrt{5}=2+0\sqrt{5}$

On comparing both sides, we get

$a=2,b=0$

Therefore, the value of a is 2 and the value of b is equal to 0.