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√(5)` is
`(√(5)+√(3))(√(5)-√(3))`.

To find:

The values of a and b.

Solution:

According to the given information,

`a+b√(5)=(√(5)+√(3))(√(5)-√(3))`

`a+b√(5)=(√(5))^2-(√(3))^2`
`[\because a^2-b^2=(a-b)(a+b)]`

`a+b√(5)=5-3`

`a+b√(5)=2`

It can be written as

`a+b√(5)=2+0√(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.