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Question
If a – b = 6 and ab = 16, find a2 + b2
Solution
(a − b)2 = a2 + b2 − 2ab
⇒ (6)2 = a2 + b2 − 2×16
⇒ 36 = a2 + b2 − 32
⇒ 36 + 32 = a2 + b2
⇒ 68 = a2 + b2
∴ a2 + b2 = 68
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