cat 2022 Question 15

Question

Let a and b be natural numbers. If $a^2+a b+a=14$ and $b^2+a b+b=28$, then (2a + b) equals

Accepted Answer

a(a + b + 1) = 14 …… (1)

b(a + b + 1) = 28 …… (2)

$\frac{a}{b} = \frac{1}{2}$

b = 2a

Substituting in (1), we get

a(3a + 1) = 14

$3a^2 + a - 14 = 0$

$3a^2 - 6a + 7a - 14 = 0$

$3a(a - 2) + 7(a - 2) = 0$

Given, a and b are natural numbers.

Therefore, a = 2 and b = 4

2a + b = $2(2) + 4 = 8$

Question 15.