(x+y)+(y+z)=5(x+y)(y+z)

Question

(x+z)+(y+z)=7(y+z)(x+z)
(x+y)+(x+z)=6(z+x)(x+y)
find xyz please show working

Answer 1

My previous solution of x=y=z=0 works, but was derived in error.

The other solution is
x = 5/24
y = 7/24
z = 1/24

x+2y+z = 5xy + 5xz + 5y^2 + 5yz
x+y+2z = 7xy + 7xz + 7yz + 7z^2
2x+y+z = 6x^2 + 6xy + 6xz + 6yz

Now just start substituting.

Answer 2

both how did u solved it Sir steve