[a/2+b/2]^2+[a/2-b/2]^2=

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[a/2+b/2]^2+[a/2-b/2]^2=
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[a/2+b/2]^2+[a/2-b/2]^2=
[a/2+b/2]^2+[a/2-b/2]^2=

[a/2+b/2]^2+[a/2-b/2]^2=
[a/2+b/2]^2+[a/2-b/2]^2
=2*[(a/2)^2+(b/2)^2]
=a^2/2+b^2/2

直接展开就可以了,答案:(a^2+b^2)/2