Question

If x +y + z = 7 and xy + yz + zx = 6 then x ^2 + y^2+ z^2 ​

Answer 1

Answer:

$x^{2} + y^{2} + z^{2} = 37$

Step-by-step explanation:

$(x+y+z)^{2} = x^{2} + y^{2} + z^{2} +2xy+2yz+2xz\\\\7^{2} = x^{2} + y^{2} + z^{2} + 2(xy+yz+zx)\\\\49 = x^{2} + y^{2} + z^{2} +2 X 6\\\\49 - 12 = x^{2} + y^{2} + z^{2}\\\\\\.: x^{2} + y^{2} + z^{2} = 37$

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