设非零复数x,y满足x^2+xy+y^2=0.则代数式[x/(x+y)]^2010-[y/(x+y)]^2010=?
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:2024/07/13 05:28:24
设非零复数x,y满足x^2+xy+y^2=0.则代数式[x/(x+y)]^2010-[y/(x+y)]^2010=?
![设非零复数x,y满足x^2+xy+y^2=0.则代数式[x/(x+y)]^2010-[y/(x+y)]^2010=?](/uploads/image/z/16436105-17-5.jpg?t=%E8%AE%BE%E9%9D%9E%E9%9B%B6%E5%A4%8D%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3x%5E2%2Bxy%2By%5E2%3D0.%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8F%5Bx%2F%28x%2By%29%5D%5E2010-%5By%2F%28x%2By%29%5D%5E2010%3D%3F)
x^2+xy+y^2=0,两边除以y^2得,(x/y)^2+x/y+1=0,根据求根公式得,x/y=(-1+√3i)/2,或x/y=(-1-√3i)/2,当x/y=(-1+√3i)/2时,x/(x+y)=1-y/(x+y)=1-1/(x/y+1)=(1+√3i)/2,y/(x+y)=(1-√3i)/2,当x/y=(-1-√3i)/2时,x/(x+y)=(1-√3i)/2,y/(x+y)=(1+√3i)/2,两种情况都是[x/(x+y)]^2010-[y/(x+y)]^2010=[(1-√3i)/2]^2010+[(1+√3i)/2]^2010,计算[(1-√3i)/2]^3=-1,[(1+√3i)/2]^3=-1,所以原式=(-1)^670+(-1)^670=1+1=2
整数x,y满足方程2xy+x+y=83,则x+y怎么算
若正实数x.y满足x+y=xy,则x+2y的最小值
已知xy/x+y=2,则代数式3x-5y+8y/-x+3xy-y的值
若(x*x+y*y)(x*x+y*y)-4x*x*y*y=0,求代数式(x*x+5xy+y*y)/(x*x+2xy+y*
已知x+y=-1,xy=-2,求代数式-5(x+y)+(x-y)+x(xy+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y-2x=0.求代数式(x^2-y^2)(x^2-xy+y^2)/(x^2+xy+y^2)(x^2-y^2).
设非零复数x,y满足x平方加xy加y平方=0,则代数式(x加y分之x)的1996次方加(x加y分之y)的1996次方的值
已知xy/x+y=1/2,则代数式3x-5xy+3y/-x+3xy-y=
若实数x,y满足根号x-2 +(3-y)^2=0,则代数式xy-x的值为
利用x-y=3^2009,xy=-3^2010,求代数式:(2x+3y-2xy)-(x+4y+xy)-(3xy+2y-2
已知X-Y/X+Y=3,求代数式2(x-y)/X+Y-3X+Y/X+Y