Đáp án:
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`a,`
`x^2 + 10x + 26 + y^2 + 2y`
`= x^2 + 10x + 25 + y^2 + 2y + 1`
`= [x^2 + 10x + 25] + [y^2 + 2y + 1]`
`= [x^2 + 2 . 5x + 5^2] + [y^2 + 2 . 1y + 1^2]`
`= (x+5)^2 + (y+1)^2`
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`b,`
`x^2 - 6x + 13 + y^2 + 2y`
`= x^2 - 6x +9 + y^2 + 2y + 1 + 3`
`= [x^2-6x+9] + [y^2+2y+1] + 3`
`= [x^2 - 2 . 3x + 3^2] + [y^2 + 2 . 1y + 1^2] + 3`
`= (x-3)^2 + (y + 1)^2 + 3`
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`c,`
`4x^2 - 4x + 1 + 2z^2 - 2z`
`= 4x^2 - 4x + 4 + 2z^2 - 2z + 1 - 4`
`= [4x^2 - 4x + 4] + [2z^2 - 2z + 1]-4`
`= 4 [x^2 -x + 1] + 2 [z^2 - z + 1/2]-4`
`= 4 [x^2 - 2 . 1/2x + 1/4 + 3/4] + 2[ z^2 - 2 . 1/2z + 1/4 + 1/4] - 4`
`= 4 [x^2 - 2 . 1/2x + (1/2)^2 + 3/4] + 2 [z^2 - 2 . 1/2z + (1/2)^2 + 1/4] - 4`
`= 4 (x-1/2)^2 + 3 + 2 (z-1/2)^2 + 1/2-4`
`= 4 (x-1/2)^2 + 2 (z-1/2)^2 + (3 + 1/2-4)`
`= 4 (x-1/2)^2 + 2 (z-1/2)^2 -1/2`
