Question

x/y+z=y/z+x=z/x+y=k prove that k=- if x+y+z not equal to zero​

Answer 1

1+ x/(y+z)= k+1

1+y/(x+z)= k+1

1+ z/(x+y)= k+1

(y+z)/(x+y+z)=1/(k+1)

(x+z)/(x+y+z)=1/(k+1)

(x+y)/(x+y+z)= 1/(k+1)

on adding above three equations

2(x+y+z)/(x+y+z)=3/(k+1)

k+1=3/2

k=1/2 [ans]

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