Ta có:
` x + y + z = 3 `
` => (x + y + z)^{2} = 3^{2} `
` => x^{2} + y^{2} + z^{2} + 2(xy + yz + xz) = 9 `
Thay ` x^2 + y^2 + z^2 = 17, ` ta có:
` 17 + 2(xy + yz + xz) = 9 `
` => 2(xy + yz + xz) = -8 `
` => xy + yz + xz = -4 `
` => 1/x + 1/y + 1/z = \frac{-4}{xyz} `
` => \frac{-4}{xyz} = 1/3 `
` => xyz = -12 `