Question

If x+y+z=7 and

1/x + 1/y + 1/z =10+xyz ,then find the value of x^2+y^2+z^2+1

Answer 1

(x+y+z)^2 = x^2+y^2+z^2 + 2xy+2xz+2yz = 7^2

x^2+y^2+z^2 + 2xyz (xy+xz+yz)/xyz = 49
x^2+y^2+z^2 + 2xyz (1/z + 1/y + 1/x) = 49
see what you can do with that.