答案是20
S=(2x-y) 2+( 2y-z) 2 +(2z-x) 2
= 4x⒉+y⒉-4xy+4y⒉+z⒉-4yz+4z⒉+x⒉-4xz
=5(x⒉+y⒉+z⒉)-4(xy+yz+zx)
=5*4-4(xy+yz+zx)
=20-4(xy+yz+zx)
S最大时(xy+yz+zx)为0
所以S最大为20
答案是20
S=(2x-y) 2+( 2y-z) 2 +(2z-x) 2
= 4x⒉+y⒉-4xy+4y⒉+z⒉-4yz+4z⒉+x⒉-4xz
=5(x⒉+y⒉+z⒉)-4(xy+yz+zx)
=5*4-4(xy+yz+zx)
=20-4(xy+yz+zx)
S最大时(xy+yz+zx)为0
所以S最大为20