Đáp án:
Giải thích các bước giải:
`x^6-x^5+x^4-x^3+x^2-x+\frac{3}{4}`
`=(x^6-x^5+\frac{x^4}{4})+(\frac{3}{4}x^4-x^3+\frac{1}{3}x^2)+(\frac{2}{3}x^2-x+\frac{3}{8})+\frac{3}{8}`
`=x^4(x^2-x+\frac{1}{4})+\frac{3}{4}x^2(x^2-\frac{4}{3}x+\frac{4}{9})+\frac{2}{3}(x^2-\frac{3}{2}x+\frac{9}{16})+\frac{3}{8}`
`=x^4(x-\frac{1}{2})^2+\frac{3x^2}{4}(x-\frac{2}{3})^2+\frac{2}{3}(x-\frac{3}{4})^2+\frac{3}{8}>0`
`⇒x^6-x^5+x^4-x^3+x^2-x+\frac{3}{4}>0∀x` (đpcm)
