Question

设x,y,z属于R求证x的平方加y的平方加z的平方大于等于xy+yz+zx

Answer 1

(x-y)^2+(y-z)^2+(z-x)^2≥0

x^2-2xy+y^2+y^2-2yz+z^2+z^2-2zx+x^2≥0

2(x^2+y^2+z^2)-2(xy+yz+zx)≥0

2(x^2+y^2+z^2)≥2(xy+yz+zx)

x^2+y^2+z^2≥xy+yz+zx