a

b

=

(where b ≠ 0)

Squaring both sides, we get

[

=

[ ]

2

2

+

5

+

=

a²

b²

7

+

=

=

–

7

=

a²

b²

–

7b²

=

a²

2

–

7b²

Sol.

So, there exist co-prime integers a and b such that

∴

∴

∴

∴

∴

∴

Q.

]²

We know, (a + b)² = (a² + b² + 2ab)

a

b

2

b²

Here,

is an rational number

This implies,

∴

Therefore, there is a contradiction and our assumption is wrong

∴

Sol.

Q.

a

b

=

(where b ≠ 0)

So, there exist co-prime integers a and b such that