a,x^2 + x+ 1 >0 mọi x thuộc R b, -4x^2 -4x - 2 < 0 mọi x thuộc R c, x^2 + 4y^2 + z^2 - 2X -6z + 8y + 15 > 0 mọi x,y,z thuộc R

`a)`

`x^2 + x + 1`

` = (x^2+x+1/4) + 3/4`

`=  (x+1/2)^2 + 3/4 \ge 3/4  >  0 \forall x \in RR`

Hay `x^2+x+1>0\forall x\in RR`

`b)`

`-4x^2  - 4x - 2`

` = - (4x^2 + 4x + 1) - 1 `

` = - (2x+1)^2 - 1 \le -1 < 0 \forall x \in RR`

Hay `-4x^2-4x-2 < 0 \forall x \in RR`

`c)`

`x^2 + 4y^2 + z^2 - 2x - 6z + 8y + 15`

` = (x^2-2x+1) + (4y^2+8y+4) + (z^2 - 6z + 9)  + 1`

` = (x-1)^2 + 4 (y+1)^2 + (z-3)^2 + 1 \ge 1 > 0 \forall x ; y ; z \in RR`

Hay `x^2 + 4y^2 + z^2 - 2x - 6z + 8y + 15 > 0 \forall x ; y ; z \in RR`