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Question
If m – n = 16 and m2 + n2 = 400, then find mn.
Solution
Given, m – n = 16 and m2 + n2 = 400.
Since, (m – n)2 = m2 + n2 = 2mn ...[Using the identity, (a – b)2 = a2 + b2 – 2ab]
∴ (16)2 = 400 – 2mn
⇒ 2mn = 400 – (16)2
⇒ 2mn = 400 – 256
⇒ 2mn = 144
⇒ `mn = 144/2`
⇒ mn = 72
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