abc为正数 a+b=1 求证axx+byy>或等于(ax+by)(ax+by)
问题描述：
abc为正数 a+b=1 求证axx+byy>或等于(ax+by)(ax+by)
答
ax^2+by^2-(ax+by)^2
=ax^2+by^2-(a^2x^2+2abxy+b^2y^2)
=a(1-a)x^2-2abxy+b(1-b)y^2
=abx^2-2abxy+bay^2
=ab(x^2-2xy+y^2)
=ab(x-y)^2
>=0
所以ax^2+by^2>=(ax+by)^2