Bài 5:
a) Ta có: \(\left|x+\dfrac{15}{19}\right|\ge0\forall x\)
Dấu '=' xảy ra khi \(x=-\dfrac{15}{19}\)
Vậy: \(M_{min}=0\) khi \(x=-\dfrac{15}{19}\)
b) Ta có: \(\left|x-\dfrac{4}{7}\right|\ge0\forall x\)
\(\Leftrightarrow\left|x-\dfrac{4}{7}\right|-\dfrac{1}{2}\ge-\dfrac{1}{2}\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{4}{7}\)
Vậy: \(N_{min}=-\dfrac{1}{2}\) khi \(x=\dfrac{4}{7}\)
Bài 6:
a) Ta có: \(\left|\dfrac{5}{3}-x\right|\ge0\forall x\)
\(\Leftrightarrow-\left|\dfrac{5}{3}-x\right|\le0\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{5}{3}\)
Vậy: \(P_{max}=0\) khi \(x=\dfrac{5}{3}\)
b) Ta có: \(\left|x-\dfrac{1}{10}\right|\ge0\forall x\)
\(\Leftrightarrow-\left|x-\dfrac{1}{10}\right|\le0\forall x\)
\(\Leftrightarrow-\left|x-\dfrac{1}{10}\right|+9\le9\forall x\)
Dấu '=' xảy ra khi \(x=\dfrac{1}{10}\)
Vậy: \(Q_{max}=9\) khi \(x=\dfrac{1}{10}\)
