xy+yz+xz的最小值为x2+y2=3,y2+z2=4,x2+z2=5则xy+yx+xz的最小值为(是最小值!)

Question

xy+yz+xz的最小值为
x2+y2=3,y2+z2=4,x2+z2=5 则xy+yx+xz的最小值为(是最小值!)

Answer 1

(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)≥0
(3+4+5)/2+2(xy+yz+zx)≥0
xy+yx+xz≥-3