Correct option is (c) 1
Given that
a = (√5 + √4)–3 & b = (√5 – √4)–3
∴ ab = (√5 + √4)–3 x (√5 – √4)–3
= (5−4)−3
= 1
∴ (a + 1)−1 + (b + 1)−1
\(= \frac 1{a + 1} + \frac 1{b + 1}\)
\(= \frac{a + b + 2}{ab + a + b + 1}\)
But ab = 1.
So,
\( \frac{a + b + 2}{ab + a + b + 1} = \frac{a + b + 2}{ a + b + 2} = 1\)