Đáp án+Giải thích các bước giải:
`3x^2-5x+3` `=x^2+x^2+x^2-2x-2x-x+1+1+1/4+3/4`
`=(x^2-2x+1+x^2)-2x+1+x^2-x+4/4`
`=x^2-2x+1+x^2-2x+1+x^2-x+1/4+3/4`
`=(x^2-2.x.1+1^2)+(x^2-2x.1+1^2)+[x^2-2.x.1/2+(1/2)^2]+3/4`
`=(x^2-2x+1)+(x^2-2x+1)+(x^2-x+1/4)+3/4`
`=(x+1)^2+(x+1)^2+(x+1/2)^2+3/4`
`=2(x+1)^2+(x+1/2)^2+3/4`
Lại có:
`2(x+1)^2≥0∀x`
`(x+1/2)^2≥0∀x`
`=>=2(x+1)^2+(x+1/2)^2+3/4≥0∀x`
`=>2(x+1)^2+(x+1/2)^2≥3/4(đcpcm)`
Xin hay nhất
