`a) x^2 - 4x + 5 `
`<=> x^2 - 4x + 4 + 1`
`<=> ( x-2)^2 + 1`
`1 > 0 ; ( x - 2 )^2 ≥ 0`
`<=> ( x-2)^2 + 1 ≥ 0 ∀ x ( ĐPCM )`
` b) 4x^2 - 20x + 27`
`<=>( 2x)^2 - 20x + 25 + 2`
`<=> ( 2x - 25 )^2 + 2`
`2 > 0 ; ( 2x-25)^2 ≥ 0`
`<=> ( 2x-25)^2 + 2 ≥ 0 ∀ x ( ĐPCM )`
` c) 2x^2 + 2x + 5`
`<=> ( x^2 + 2x + 1 ) + x^2 + 4`
`<=> ( x + 1 )^2+ x^2 + 4`
`( x+1)^2 ≥ 0 ; x^2 ≥ 0 ; 4 > 0`
`<=> ( x + 1 )^2+ x^2 + 4 ≥ 0 ∀ x ( ĐPCM )`
` d) x^2 + 4x + y^2 - 6y + 15`
`<=> ( x^2 + 4x + 4 ) + ( y^2 - 6y + 9 ) + 2`
`<=> ( x + 2 )^2 + ( y - 3 )^2 + 2`
`( x+2)^2 ≥ 0 ; ( y - 3)^2 ≥ 0 ; 2 > 0`
`=> ( x + 2 )^2 + ( y - 3 )^2 + 2 > 0 ∀ x , y ( ĐPCM)`
