Question

chứng minh x^2 - x + 1/3 luôn đúng

Answer 1

Ta có :

\(x^2-x+1=x^2-2.x.\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-\dfrac{1}{4}+1\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\left(\left(x-\dfrac{1}{2}\right)^2\ge0,\forall x\in R\right)\)

\(\Rightarrow\dfrac{x^2-x+1}{3}\ge\dfrac{1}{3}.\dfrac{3}{4}=\dfrac{1}{4},\forall x\in R\)

Vậy \(đpcm\)

Answer 2

Luôn đúng là sao em nhỉ? Chắc đề là \(x^2-x+\dfrac{1}{3}>0\) luôn đúng?