Question

6. If x/y+z=y/z+x=z/x+y=k prove that k= -, if (x+y+z)≠0​

Answer 1

Step-by-step explanation:

taking k=1/2

x,y,z is not equal to zero

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]

you can take the value of k like this and solve