Find all real solutions to the equation ?
Find all real solutions to the equation
- atsuoLv 62 months 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) .