代入左侧得[(x1+x2)/2]^2+a(x1+x2)/2+b
代入右侧得[(x1)^2+(x2)^2]/2+a(x1+x2)/2+b
即证明:
[(x1+x2)/2]^2+a(x1+x2)/2+b≤[(x1)^2+(x2)^2]/2+a(x1+x2)/2+b,
整理得:
即证明:
[(x1+x2)/2]^2≤[(x1)^2+(x2)^2]/2,
左右整理合并同类项,即证明:
(x1)^2+(x2)^2-2(x1)(x2)≤0
配方得:
(x1-x2)^2≤0,得证
代入左侧得[(x1+x2)/2]^2+a(x1+x2)/2+b
代入右侧得[(x1)^2+(x2)^2]/2+a(x1+x2)/2+b
即证明:
[(x1+x2)/2]^2+a(x1+x2)/2+b≤[(x1)^2+(x2)^2]/2+a(x1+x2)/2+b,
整理得:
即证明:
[(x1+x2)/2]^2≤[(x1)^2+(x2)^2]/2,
左右整理合并同类项,即证明:
(x1)^2+(x2)^2-2(x1)(x2)≤0
配方得:
(x1-x2)^2≤0,得证