Question

If a - 3b = 2 and a²- 4ab + 3b² − 24  = 0, then what is 'a + b' equal to

1. 27
2. 22
3. 25
4. 19

Answer 1

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.