已知x⼀(y+z)=y⼀(z+x)=z⼀(x+y) 求(x+y)⼀z的值

2025-05-09 16:03:10
推荐回答(3个)
回答1:

x/(y+z)=y/(z+x)=z/(x+y)=(x+y+z)/(2x+2y+2z)=1/2,z/(x+y)=1/2,(x+y)/z=2。

回答2:

x/(y+z)=y/(z+x)=z/(x+y)
x/(y+z)=y/(z+x)
xz+x²=y²+yz
x²-y²=yz-xz
(x+y)(x-y)=z(y-x)
当x=y时,由于他们是对称的,所以x=y=z,z分之x+y=(x+y)/z=2
当x≠y时,x+y=-z,(x+y)/z=-1

回答3:

x/(y+z)=y/(y+x)=>y2+yz=x2+xz=>x2-y2=yz-xz=>(x+y)(x-y)=z(y-x)=(x+y)/z=-1