Question

Answer 1

`1)A=x^2+2x+2=x^2+2x+1+1=(x+1)^2+1 >= 1 > 0 AA x`

     `->` đpcm

`2)B=x^2+4x+6=x^2+4x+4+2=(x+2)^2+2 >= 2 > 0 AA x`

     `->` đpcm

`3)C=x^2-x+1=x^2-2.x. 1/2+1/4+3/4=(x-1/2)^2+3/4 >= 3/4 > 0 AA x`

    `->` đpcm

`4)D=x^2+x+1=x^2+2.x. 1/2+1/4+3/4=(x+1/2)^2+3/4 >= 3/4 > 0 AA x`

    `->` đpcm

`5)E=x^2+3x+3=x^2+2.x. 3/2+9/4+3/4=(x+3/2)^2+3/4 >= 3/4 > 0 AA x`

    `->` đpcm

`6)F=2x^2+4x+3=2(x^2+2x+3/2)=2(x^2+2x+1+1/2)=2[(x+1)^2+1/2]`

                     `=2(x+1)^2+1 >= 1 > 0 AA x`

    `->` đpcm

`7)G=3x^2-5x+3=3(x^2+5/3x+1)=3(x^2+2.x. 5/6+25/36+11/36)=3[(x+5/6)^2+11/36]`

                            `=3(x+5/6)^2+11/12 >= 11/12 > 0 AA x`

      `->` đpcm

`8)H=4x^2+4x+2=4x^2+4x+1+1=(2x+1)^2+1 >= 1 > 0 AA x`

   `->` đpcm

`9)K=4x^2+3x+2=4x^2+2.2x. 3/4+9/16+23/16`

                        `=(2x+3/4)^2+23/16 >= 23/16 > 0 AA x`

`10)L=2x^2+3x+4=2(x^2+3/2+2)=2(x^2+2.x. 3/4+9/16+23/16)=2[(x+3/4)^2+23/16]`

                    `=2(x+3/4)^2+23/8 >= 23/8 > 0 AA x`

   `->` đpcm