100/(x-y)+100/(x+y)=100/y 怎么解

来源：百度知道 编辑：UC知道 时间：2024/09/12 17:06:49
100/(x-y)+100/(x+y)=100/y

怎么解出 x=(1+根号2)y ?

100/(x-y)+100/(x+y)=100/y
1/(x-y)+1/(x+y)=1/y
通分
(x+y+x-y)/(x+y)(x-y)=1/y
2x/(x+y)(x-y)=1/y
对角相乘
2xy=(x+y)(x-y)=x^2-y^2
x^2-2xy-y^2=0
把y看成已知
则x^2-2xy+y^2=2y^2
(x-y)^2=2y^2=(±√2y)^2
x-y=±√2y
x=y±√2y=(1±√2)y

约分得1/(X-Y)+1/(X+Y)=1/Y
同时乘以(X-Y)(X+Y)Y得
Y(X+Y)+Y(X-Y)=(X+Y)(X-Y）
化简 2XY=X^2-Y^2
遗式 X^2-2XY-Y^2+(Y^2-Y^2)=0
(X+Y)^2=2Y^2
X+Y=√（2Y^2）=±Y√2
X=±Y√2-Y=±Y(√2-1)

解：由100/(x-y)+100/(x+y)=100/y
得100/(x+y)+100/(x-y)=100/(x+y)(x-y)y
所以 100/y=100/(x+y)(x-y)y
所以(x+y)(x-y)=1
所以X=根号下（1+y^2）

你给的答案不对

100/(x-y)+100/(x+y)=100/y
先约分，得1/(x-y)+1/(x=y)=1/y

再通分得：2x/(x^2-y^2)=1/y
去分母得：x^2-2xy-y^2=0
将这个方程看成关于x的一元二次方程，运用求根公式，解得x=(1+根号2)y
此题得解

给我分，他分太多，这是我原创，没抄袭他！
100/(x-y)+100/(x+y)=100/y
200x/x^2-y^2=100/y
x^2-y^2=2xy
x^2-2xy+y^2-2y^2=0
(x-y)^2=2y^2
x-y=±√2y