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Question
Show that (m – n)2 + (m + n)2 = 2(m2 + n2)
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Solution
Taking the L.H.S = (m – n)2 + (m + n)2
= m2 – 2mn + n2 + m2 + 2mn + n2
= m2 + n2 + m2 + n2
= 2m2 + 2n2 ...`[∵ {:(("a" + "b")^2 - 4"ab" = "a"^2 + 2"ab" + "b"^2),(("a" - "b")^2 = "a"^2 - 2"ab" + "b"^2)]`
= 2(m2 + n2)
= R.H.S
∴ (m – n)2 + (m + n)2 = 2(m2 + n2)
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