If `(y-z)prop1/x, (z-x)prop and (x-y)prop1/z,` then find the sum of three variation constants .

Explanation

`(y-z) prop1/x rArry-z =k_(1). 1/x(where k_(1)ne0="variation constant".)`
`rArr k_(1) =x(y-z)…..(1) `
`(z-x) prop1/y , therefore(z-x)=k_(2). 1/y(where k_(2)ne0="variation constant" )`
`therefore k_(2) =y (z-x) …….(2) `
Also , `(x-y) prop1/z , therefore x-y =k_(3) x 1/z(" where " k_(3) ne0= "variation constant")`
`therefore k_(3) =z(x-y)......(3)`
Now , adding (1) +(2) +(3) we get ,
`k_(1)+k_(2)+k_(3) =x(y-z)+y(z-x)+z(x-y)`
`=xy-xz+yz-xy+zx-yz=0`
`therefore k_(1) +k_(2)+ k_(3) =0.`
Hence the sum of three variation constant =0.