`a^2-6a+12`
`=a^2-3.2a+9+3`
`=(a-3)^2+3`
vì `(a-3)^2>=0;3>0(∀a)`
`=>(a-3)^2+3>=3`
hay `a^2-6a+12>0(∀a)`
`b)(x-3)(x-5)+10>0`
`=x^2-5x-3x+15+10`
`=x^2-8x+25`
`=x^2-2.4x+16+9`
`=(x-4)^2+3`
vì `(x-4)^2>=0;3>0(∀x)`
`=>(x-4)^2+3>0`
vậy `(x-3)(x-5)+10>0(∀x)`
`c)a^2+a+1`
`=a^2+2.1/2a+1/4+3/4`
`=(a+1/2)^2+3/4`
vì `(a+1/2)^2>=0;3/4>0(∀a)`
`=>(a+1/2)^2+3/4>0(∀a)`
`=>a^2+a+1>0`
`d)-x^2-5x-25<0`
`=-(x^2+2.5/2x+25/4+125/4)`
`=-[(x+5/2)^2+125/4]`
vì `(x+5/2)^2>=0;125/4>0(∀x)`
`=>(x+5/2)^2+125/4>0`
`=>-[(x+5/2)^2+125/4]<0(∀x)`
hay `-x^2-5x-25<0`
xin hay nhất ạ