设非零复数x,y满足x^2+xy+y^2=0,求代数式(x/x+y)^1990+(y/x+y)^1990的值
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/05/04 03:02:17
设非零复数x,y满足x^2+xy+y^2=0,求代数式(x/x+y)^1990+(y/x+y)^1990的值
x^2=-y(x+y)
y^2=-x(x+y)
所以x/(x+y)=-y/x
y/(x+y)=-x/y
而(x/y)^2+x/y+1=0
所以(x/y)^3=1
同样(y/x)^3=1`
所以[x/(x+y)]^1990+[y/(x+y)]^1990
=(y/x)^1990+(x/y)^1990
=(y/x)^2+(x/y)^2
=-1-y/x-1-x/y
=-2-(x^2+y^2)/xy
=-1
y^2=-x(x+y)
所以x/(x+y)=-y/x
y/(x+y)=-x/y
而(x/y)^2+x/y+1=0
所以(x/y)^3=1
同样(y/x)^3=1`
所以[x/(x+y)]^1990+[y/(x+y)]^1990
=(y/x)^1990+(x/y)^1990
=(y/x)^2+(x/y)^2
=-1-y/x-1-x/y
=-2-(x^2+y^2)/xy
=-1
已知实数x,y满足关系式│x+y-3│+根号(xy-6)=0,求代数式(x+2y)/y-x的值
已知x+y=-1,xy=-2,求代数式-5(x+y)+(x-y)+x(xy+y)的值
正数x,y满足x^2-y^2=2xy,求(x-y)/(x+y)的值
已知xy满足x^2+y^2+4/5=2x+y 求代数式yx/x+y的值
已知x,y满足x^2+y^2-2x-y+5/4=0,求代数式xy(x+y)的值
已知实数x、y满足关系式绝对值x+y-7绝对值+根号(xy-6)=0,求代数式(x+2y)/(y-x)的值
已知x,y满足x²+y²+5/4=2x+y,求代数式xy/(x+y)的值.
已知x*x-4xy+4y*y=0 求[2x(x+y)-y(x+y)]/(4x*x-4xy+y*y)的值?
正整数x,y满足x2-y2=2xy,求x-y/x+y的值
整数x,y满足x2-y2=2xy,求x-y/x+y的值
已知x+y=-1,xy=-2,求代数式-5(x+y)+(x-y)+2(xy+y)的值
已知X+Y=-1,xy=-2,求代数式-5(x+y)+(x-y)+(xy+y)的值