问题
填空题
已知x,y为实数,则代数式2x2+2xy+y2-2x-1的最小值为______
答案
∵2x2+2xy+y2-2x-1,
=(x2+2xy+y2)+(x2-2x+1)-2,
=(x+y)2+(x-1)2-2≥-2.
∴2x2+2xy+y2-2x-1最小值为-2.
已知x,y为实数,则代数式2x2+2xy+y2-2x-1的最小值为______
∵2x2+2xy+y2-2x-1,
=(x2+2xy+y2)+(x2-2x+1)-2,
=(x+y)2+(x-1)2-2≥-2.
∴2x2+2xy+y2-2x-1最小值为-2.