Question

Tìm gtln,  gtnn của |3x+7|+13/2.|3x+7|+6

Answer 1

\(A=\left|3x+7\right|+\frac{13}{2}\left|3x+7\right|+6\)

Có: \(\left|3x+7\right|\ge0;\frac{13}{2}\left|3x+7\right|\ge0\)

\(\Rightarrow\left|3x+7\right|+\frac{13}{2}\left|3x+7\right|+6\ge6\)

Dấu '=' xảy ra khi: \(\left|3x+7\right|+\frac{13}{2}\left|3x+7\right|=0\)

\(\Leftrightarrow\left|3x+7\right|.\left(\frac{13}{2}+1\right)=0\)

\(\Leftrightarrow\left|3x+7\right|=0\Leftrightarrow3x+7=0\)

 \(\Leftrightarrow x=-\frac{7}{3}\)

Vậy: \(Min_A=6\) tại \(x=-\frac{7}{3}\)