已知3x+4y=25,当x= 时,函数f（x,y）=x^2+y^2有 值为 .

y=(25-3x)/4
f(x,y)=x^2+(25-3x)^2/16=x^2+9x^2+625-150x
= 10x^2 -150x +625 = 10(x^2 -37.5x + 62.5)=10(x^2 - 2*18.75x +351.5625-
-351.5625+62.5)=10[(x-18.75)^2-289.0625]
f(x,y) = 10[(x-18.75)^2-289.0625]
即：x = 18.75 时,f（x,y）有最小值：－2890.625.