# Find all real solutions to the equation ?

Find all real solutions to the equation

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- atsuoLv 63 weeks ago
3x^2 + y^2 + z^2 = 2x(y + z)

x^2 - 2xy + y^2 + x^2 - 2xz + z^2 + x^2 = 0

(x - y)^2 + (x - z)^2 + x^2 = 0

x , y and z must be real , so three terms in the left side are

all non-negative . Therefore

x - y = 0 , x - z = 0 and x = 0 .

That is , (x,y,z) = (0,0,0) .

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A real number becomes non-negative when it is squared .

So (x - y)^2 , (x - z)^2 and x^2 are all non-negative .