Đáp án + Giải thích các bước giải:
`x^2 + y^2 + z^2 - xy - yz - zx = 0`
`=> 2 ( x^2 + y^2 + z^2 - xy - yz - zx ) = 0`
`2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2zx = 0`
`( x^2 - 2xy + y^2 ) + ( y^2 - 2yz + z^2 ) + ( z^2 - 2zx + x^2 )= 0`
`( x - y )^2 + ( y - z )^2 + ( z - x )^2 = 0`
`\text{mà} {( ( x - y )^2 >= 0 ),( ( y - z )^2 >= 0 ),( ( z - x )^2 >= 0 ):}`
`=> {( ( x - y )^2 = 0 ),( ( y - z )^2 = 0 ),( ( z - x )^2 = 0 ):}`
`=> {( x - y = 0 ),( y - z = 0 ),( z - x = 0 ):}`
`=> {( x = y ),( y = z ),( z = x ):}`
`=> x = y = z ( đpcm )`
