(x-2)^2+(x-y+1)^2+(3x-y-5)^2的最小值
问题描述:
(x-2)^2+(x-y+1)^2+(3x-y-5)^2的最小值
答
答案是1吗?
x=3,y=4.
答
利用a²+b²≥(a+b)²/2(x-2)^2+(x-y+1)^2+(3x-y-5)^2=(x-2)^2+(x-y+1)^2+(y-3x+5)^2≥(x-2)^2+((x-y+1)+(y-3x+5))²/2…………( x-y+1=y-3x+5时取得等号)=(x-2)^2+(-2x+6)²/2=3x²...