已知x-y=3,求x²+2x-y的最小值,
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已知x-y=3,求x²+2x-y的最小值,
已知x-y=3,求x²+2x-y的最小值,
已知x-y=3,求x²+2x-y的最小值,
x=3+y
带入
(9+6y+y²)+2(3+y)-y
=y²+7y+15
=(y+7/2)²+15-49/4
最小值11/4
将y=x-3带入,结果也是一样的
y=x-3
x²+2x-y=x²+2x-(x-3)=x²+x+3
对称轴为x=-1/2,x=-1/2时取得最小值11/4.
令y=x-3;
x²+2x-y
=x²+2x-(x-3)
=x²+x+3
=(x+1/2)²+11/4大于等于11/4
答案是11/4
已知x-y=3,
则,x=3+y
x^2+2x-y
=(3+y)^2+2(3+y)-y
=9+6y+y^2+6+2y-y
=y^2+7y+15
=(y+7/2)^2-49/4+15
=(y+7/2)^2+11/4
而(y+7/2)^2>=0
所以,它的最小值11/4