Question

if x/y+z = y/z+x = z/x+y then show that each ratio is 1/2.​

Answer 1

Answer:

each ratio is `1/2,-1`

Solution:

Here `x/(y+z)=y/(z+x)=z/(x+y)`

Case-1 : If `x+y+z!=0`, then

Each ratio`=(x+y+z)/(y+z+z+x+x+y)`

`=(x+y+z)/(2y+2z+2x)`

`=(x+y+z)/(2(y+z+x))`

Cancel the common factor `(x+y+z)`

`=(1)/(2)`

Case-2 : If `x+y+z=0`, then

`y+z=-x`

Then, the first ratio `=(x)/(y+z)`

`=(x)/(-x)`

Cancel the common factor `-x`

`=-1`

Hence, each ratio `=-1`.

Thus, the value of each ratio is `(1)/(2)` or `-1`.