Довести (m^2+n^2)/2>=m+n-1

Question

Довести (m^2+n^2)/2>=m+n-1

Answer 1

m^2+n^2-2m-2n+2=(m^2-2m+1)-1+(n^2-2n+1)-1+2=(m-1)^2+(n-1)^2

(m-1)^2>=0,(n-1)^2>=0,тогда (m-1)^2+(n-1)^2>=0.

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