Question

If x^2 + y^2 + z^2 = 250, xy + yz + zx = 3 then find x + y + z .

Answer 1

given,

${x}^{2} + {y}^{2} + {z}^{2} = 250 \\ xy + yz + xz = 3 \\ then \\ \: {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2(xy + yz + xz) \\ = {(x + y + z)}^{2} = 250 + 2 \times 3 \\ = {(x + y + z)}^{2} = 250 + 6 \\ = {(x + y + z)}^{2} = 256 \\ = (x + y + z) = \sqrt{256} \\ = x + y + z = 16$