Question

C/m rằng 2x²+5x+4luôn dương với mọi x

Answer 1

`2x^2+5x+4=2(x^2+5/2x+2)=2(x^2+2.x. 5/4+25/16+7/16)`

                             `=2[(x+5/4)^2+7/16]`

                             `=2(x+5/4)^2+7/8`

Vì `2(x+5/4)^2 >= 0 AA x`

`=>2(x+5/4)^2+7/8 >= 7/8 > 0 AA x`

Vậy `2x^2+5x+4` luôn dương với mọi `x`

Answer 2

`2x^2 +5x+4`

`=2(x^2 +5/2x+2)`

`=2(x^2 +2. 5/4 x+ 25/16 -25/16+2)`

`=2[(x^2 +5/2x+25/16+7/16]`

`=2[(x+5/4)^2 +7/16]`

`=2(x+5/4)^2 +7/8`

Do `(x+5/4)^2 >=0AAx`

`=>2(x+5/4)^2 >=0`

`=>2(x+5/4)^2 +7/8>=7/8>0`

`=>2x^2 +5x+4>0(đpcm)`