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Question
Find the values of a, b, c and d if `[(a + b, 3),(5 + c, ab)] = [(6, d),(-1, 8)]`
Solution
`[(a + b, 3),(5 + c, ab)] = [(6, d),(-1, 8)]`
Comparing the corresponding terms, we get.
3 = d ⇒ d = 3
⇒ 5 + c = – 1
⇒ c = -1 – 5
⇒ c = -6
a + b = 6 and ab = 8
∴ (a – b)2 = (a + b)2 – 4ab
= (6)2 – 4 x 8
= 36 – 32
= 4
= (±2)2
∴ a – b, b = ±2
(i) If a – b = 2
a + b = 6
Adding, we get
2a = 8
⇒ a = 4
a + b = 6
⇒ 4 + b = 6
⇒ b = 6 – 4 = 2
∴ a = 4, b = 2
(ii) If a – b = –2
a + b = 6
Adding, we get,
2a = 4
⇒ a = `(4)/(2)` = 2
a + b = 6
⇒ 2 + b = 6
⇒ b = 6 – 2 = 4
∴ a = 2, b = 4
Hence a = 4, b = 2, or a = 2, b = 4
c = –6 and d = 3.
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