设xy>=0,2x+y=6,求z=4x^2+3xy+y^2-6x-3y的最值

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/05 16:51:08

z=4x^2+3xy+y^2-6x-3y=(2x)^2+y^2+4xy-xy-3(2x+y)=(2x+y)^2-3(2x+y)-xy
=6^2-3*6-xy=18-xy
因为xy>0所以直线2x+y=6只能位于第一象限.
x：[0,3]；y：[0,6]
z=18-xy=18-x(6-2x)=2x^2-6x+18
对称轴为：x=1.5.故z的最小值为f(1.5),最大值为f(0)=f(3)

x^+2xy+y^+4=16 x^-2xy+y^=16 求(3xy+6y^)+|x^-(2xy+2y^-3x^)|的值若：X^2-4X+Y+6Y+√ Z-3+13=0求（xy)^z的值已知3x－y+2z=x+2y+3z=0,求（3x^－xy+2y^)/(2x^+4xy+y^)值? 已知xy/x+y=6,求3x-2xy+3y/-x+3xy-y的值. 若x-y=6,xy=-8,求代数式(x+y+z)²+(x-y-z)(x-y+z)-2·z(x+y)的值已知实数x,y,z满足x²-6xy+10y²+4y+|z²-3z+2|+4=0,求(x+y x+y=8,xy=-2,求(5xy+4x+7y)+(6x-3xy)-(4xy-3y)的值已知3x*+xy-2y*=0,求(x/y)-(y/x)-(x*+y*)/(xy)的值.*是平方若x+y-5xy=0,求(2x-3xy+2y)/(x+2xy+y)的值已知x-y=4xy,求x-2xy-y分之2x+3xy-2y的值! 已知y-x-2xy=0,求3x+xy-3y/y-xy-x的值已知y-x-2xy=0,求(3x+xy-3y)\(y-xy-x)的值