已知x2+4y2+x2y2-6xy+1=0,求 x4-y4/2x-y 乘 2xy-y2/xy-y2 除以(x2+y2/x
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/20 07:55:56
已知x2+4y2+x2y2-6xy+1=0,求 x4-y4/2x-y 乘 2xy-y2/xy-y2 除以(x2+y2/xy)2乘1/x+y的值
因为x²+4y²+x²y²-6xy+1=0
(x²-4xy+4y²)+(x²y²-2xy+1)=0
(x-2y)²+(xy-1)²=0
所以x-2y=0且xy-1=0
x=2y,xy=1
2y²=1,y²=1/2
x²=4y²=2
原式=[(x^4-y^4)/(2x-y)]×[(2xy-y²)/(xy-y²)]÷[(x²+y²)/(xy)]²×[1/(x+y)]
={[(x²+y²)(x+y)(x-y)]/(2x-y)}×{[y(2x-y)]/[y(x-y)]}×[(xy)²/(x²+y²)²]×[1/(x+y)] 约分
=(xy)²/(x²+y²)
=1²/(2+1/2)
=1/(5/2)
=2/5
(x²-4xy+4y²)+(x²y²-2xy+1)=0
(x-2y)²+(xy-1)²=0
所以x-2y=0且xy-1=0
x=2y,xy=1
2y²=1,y²=1/2
x²=4y²=2
原式=[(x^4-y^4)/(2x-y)]×[(2xy-y²)/(xy-y²)]÷[(x²+y²)/(xy)]²×[1/(x+y)]
={[(x²+y²)(x+y)(x-y)]/(2x-y)}×{[y(2x-y)]/[y(x-y)]}×[(xy)²/(x²+y²)²]×[1/(x+y)] 约分
=(xy)²/(x²+y²)
=1²/(2+1/2)
=1/(5/2)
=2/5
已知x2+4y2+x2y2-6xy+1=0,求 x4-y4/2x-y 乘 2xy-y2/xy-y2 除以(x2+y2/x
已知:x2+y2=4xy,求(x4+y4)÷(xy)2
已知2x=3y,求xy/(x2+y2)-y2/(x2-y2)的值
已知x+y+z=0,x2+y2+z2=1,求xy+yz+xz,x4+y4+z4的解
已知X2-2x+y2+6y+10=0,求(x2-2xy)/(xy+y2)的值
已知X2+Y2+8X+6Y+25=0 求代数式X2++XY+4Y2分之X2-4Y2 减X+2Y分之X的值
若X2+Y2-2X-6Y+10=0 ,求(x2-y2)/xy的值
已知2x-3*根号(xy)-2y=0(x>0),则x2+4xy-16y2除以2x2+xy-9y2的值是多少?
已知x2-3xy-4y2的绝对值+2倍根号x2+4xy+4y2-1=0 求3x+6y的值
已知2+4y2-4x+4y+5=0,求x四次方-y的四次方/xy乘以2x2-xy/xy-y2除以(y分之x2+y2)2
X2+Y2+8X+6Y+25=0 求代数式(x2-4y2/x2+4xy+4y2)-x/x+2y
已知xy满足x2+y2-6x+2y+10=0,求立方根号x2-y2的值