Correct Answer - Option 2 : 22
Calculation:
Here, a2- 4ab + 3b2 − 24 = 0
\(\rm ⇒a^2-4ab+(2b)^2-b^2-24=0\)
\(\rm ⇒(a-2b)^2=24+b^2\)
We have, a - 3b = 2 ⇒ a = 2 + 3b
\(⇒\rm (3b +2-2b)^2=24+b^2 \\⇒ (b+2)^2=24+b^2\\ ⇒ b^2+4b+4=24+b^2\)
\(\rm ⇒4b=20\)
⇒ b = 5
Putting, value of b in a - 3b = 2, we get
a = 2 + 3(5) = 2 + 15 = 17
∴ (a + b) = 17 + 5
= 22
Hence, option (2) is correct.