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Question
If a + b = 25 and a2 + b2 = 225, then find ab.
Sum
Solution
Given, a + b = 25 and a2 + b2 = 225
We know that,
(a + b)2 = a2 + b2 + 2ab ...[An algebraic identity]
⇒ (25)2 = 225 + 2ab
⇒ 2ab = (25)2 – 225
⇒ 2ab = 625 – 225
⇒ 2ab = 400
⇒ `ab = 400/2`
⇒ ab = 200
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