Đáp án:
d. \(Max = - 1\)
Giải thích các bước giải:
\(\begin{array}{l}
a.M = \dfrac{{3\sqrt x + 1 - 2\left( {\sqrt x - 1} \right)}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{3\sqrt x + 1 - 2\sqrt x + 2}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{{\sqrt x + 3}}{{\left( {\sqrt x + 3} \right)\left( {\sqrt x - 1} \right)}}\\
= \dfrac{1}{{\sqrt x - 1}}\\
b.Thay:x = 81\\
\to M = \dfrac{1}{{\sqrt {81} - 1}}\\
= \dfrac{1}{{9 - 1}} = \dfrac{1}{8}\\
c.M = \dfrac{3}{4}\\
\to \dfrac{1}{{\sqrt x - 1}} = \dfrac{3}{4}\\
\to 4 = 3\sqrt x - 3\\
\to 3\sqrt x = 7\\
\to \sqrt x = \dfrac{7}{3}\\
\to x = \dfrac{{49}}{9}\\
d.Do:x \ge 0\\
\to \sqrt x \ge 0\\
\to \sqrt x - 1 \ge - 1\\
\to \dfrac{1}{{\sqrt x - 1}} \le - 1\\
\to Max = - 1\\
\Leftrightarrow x = 0
\end{array}\)
