设a,b∈R+,a+b=1,求证ax^2+by^2≥(ax+by)^2

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设a,b∈R+,a+b=1,求证ax^2+by^2≥(ax+by)^2设a,b∈R+,a+b=1,求证ax^2+by^2≥(ax+by)^2设a,b∈R+,a+b=1,求证ax^2+by^2≥(ax+

设a,b∈R+,a+b=1,求证ax^2+by^2≥(ax+by)^2
设a,b∈R+,a+b=1,求证ax^2+by^2≥(ax+by)^2

设a,b∈R+,a+b=1,求证ax^2+by^2≥(ax+by)^2
x,y∈R
(x-y)2≥0
ab(x2+y2-2xy)≥0
1-a=b,1-b=a
abx2+bay2-2abxy≥0
a(1-a)x2+b(1-b)y2-2abxy≥0
(ax2-a2x2)+(by2-b2y2)-2abxy≥0
ax2+by2-(a2x2+2abxy+b2y2)≥0
ax2+by2-(ax+by)2≥0
ax2+by2≥(ax+by)2