Correct Answer - Option 2 : 49
Given:
\(\frac{√11 - 3}{√ 11 + 3} \) = a√11 + b
Formula used:
(a + b)2 = a2 + b2 + 2ab
(a + b)(a - b) = a2 - b2
Calculation:
Take L.H.S
\(\frac{√11 - 3}{√ 11 + 3} \)
Rationalisation above the equation
⇒ \(\frac{(√11 - 3) \;\times\;(√11 - 3) }{(√ 11 + 3)\; \times\;(√11 - 3)} \)
⇒ (√11 - 3)2/(11 - 9)
⇒ (11 + 9 - 6√11)/2
⇒ (20 - 6√11)/2
⇒ 10 - 3√11
Compare the above term with (a√11 + b), we get
a = - 3 and b = 10
⇒ (a + b)2 = {-3 + 10}2
⇒ (7)2
⇒ 49
∴ The required value of (a + b)2 is 49.
