If the product and sum of two quadratic surds is a rational number then surds are _______ surd. ( WBBSE – 2019 )

If the product and sum of two quadratic surds is a rational number then surds are _______ surd.

Answer : Complementary or conjugate .

Explanation :

Let us consider that { √a + b) } and { -√a + b) } are two quadratic surds, where ‘a’ and ‘b’ are two different rational numbers.

∴ sum = { √(a) + b) } + { -√a + b) }

= √a – √a + b + b

= 0 + 2b

= 2b ( a rational number )

Product = { √a + b) } { -√a + b) }

= ( b )² – ( √a )²

= b² – a