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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")]`
Solution
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.
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