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Question

Show that :
n2+(n+1)2+(n2+n)2=(n2+n+1)2

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Solution

LHS =n2+(n+1)2+(n2+n)2
=n2+n2+2n+1+n4+n2+2n3
=n4+2n3+3n2+2n+1
RHS =(n2+n+1)2
=n4+n2+1+2n3+2n2+2n
=n4+2n3+3n2+2n+1= LHS

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