Question

Find the values of a and b if A = B, where A = `[("a" + 4, 3"b"),(8, -6)]`, B = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`

Answer 1

Given that A = B

⇒ `[("a" + 4, 3"b"),(8, -6)]` = `[(2"a" + 2, "b"^2 + 2),(8, "b"^2 - 5"b")]`

Equating the corresponding elements, we get

a + 4 = 2a + 2

3b = b² + 2

b² – 5b = – 6

⇒ 2a – a = 2 

b² – 3b + 2 = 0

b² – 5b + 6 = 0

∴ a = 2

∴ b² – 3b + 2 = 0

⇒ b² – 2b – b + 2 = 0

⇒ b(b – 2) – 1 (b – 2) = 0

⇒ (b – 1)(b – 2) = 0

∴ b = 1, 2

∴ b² – 5b + 6 = 0

b² – 3b – 2b + 6 = 0

⇒ b(b – 3) – 2(b – 3) = 0

⇒ (b – 2) (b – 3) = 0

⇒ b = 2, 3

But here 2 is common.

Hence, the value of a = 2 and b = 2.