若实数a、b、c、d满足a2+b2+c2+d2=10,则y=(a-b)2+(a-c)2+(a-d)2+(b-c)2+(b-d)2+(c-d)2的最大值是_.
问题描述:
若实数a、b、c、d满足a2+b2+c2+d2=10,则y=(a-b)2+(a-c)2+(a-d)2+(b-c)2+(b-d)2+(c-d)2的最大值是______.
答
∵a2+b2+c2+d2=10,∴y=(a-b)2+(a-c)2+(a-d)2+(b-c)2+(b-d)2+(c-d)2,=a2+b2-2ab+a2+c2-2ac+b2+c2-2bc+b2+d2-2bd+c2+d2-2cd,=3(a2+b2+c2+d2)-2ab-2ac-2ad-2bc-2bd-2cd,=4(a2+b2+c2+d2)-(a+b+c+d...