\(A=3x^2-5x+4=3\times\left(x^2-2\times x\times\frac{5}{6}+\left(\frac{5}{6}\right)^2-\left(\frac{5}{6}\right)^2+\frac{4}{3}\right)=3\times\left[\left(x-\frac{5}{6}\right)^2+\frac{23}{36}\right]\)
\(\left(x-\frac{5}{6}\right)^2\ge0\)
\(\left(x-\frac{5}{6}\right)^2+\frac{23}{36}\ge\frac{23}{36}\)
\(3\times\left(\left(x-\frac{5}{6}\right)^2+\frac{23}{36}\right)\ge\frac{23}{12}>0\)
Vậy A > 0 với mọi x (đpcm)
Đúng 0
Bình luận (0)
