If x+y=5xy,y+z=6yz,z+x=7zx then find the value of x+y+z.
Let's solve these 3 equations one by one.
From x + y = 5xy, we can rewrite this as y = (x) / 5x - 1
Substitute for y in terms of x in y + z = 6yz, then we get(x) / 5x - 1 + z = 6z(x) / 5x - 1, x + z - 5z = 30z - 6z^2.
Simplify this further: x = 30z - 6z^2 + 5z = 30z - 6z^2 + 5z
Now, substitute for x in terms of z in z + x = 7zx, then we get x = z(7z - 1)
Now, equating these two expressions for x we get: 30z - 6z^2 + 5z = z (7z - 1)
After simplifying and solving for z, we get z = 5/2
Substituting this value back into x = z (7z - 1), we get x = 5/2
And y = (x) / (5x - 1), substituting in this expression the values of x and z we get y = 5/2
Thus the value of x + y + z is 5/2 + 5/2 + 5/2 = 15/2 = 7.5.