Đáp án:
Áp dụng Bunhia
$\begin{array}{l}
y = \sqrt {7 - 2x} + \sqrt {3x + 4} \left( {dkxd: - \frac{4}{3} \le x \le \frac{7}{2}} \right)\\
y = \frac{1}{{\sqrt 3 }}.\sqrt 3 .\sqrt {7 - 2x} + \frac{1}{{\sqrt 2 }}.\sqrt 2 .\sqrt {3x + 4} \\
= \frac{1}{{\sqrt 3 }}.\sqrt {21 - 6x} + \frac{1}{{\sqrt 2 }}.\sqrt {6x + 8} \\
\Rightarrow {y^2} = {\left( {\frac{1}{{\sqrt 3 }}.\sqrt {21 - 6x} + \frac{1}{{\sqrt 2 }}.\sqrt {6x + 8} } \right)^2}\\
\le \left( {\frac{1}{3} + \frac{1}{2}} \right).\left( {21 - 6x + 6x + 8} \right)\\
\Rightarrow {y^2} \le \frac{5}{6}.29 = \frac{{145}}{6}\\
\Rightarrow - \frac{{\sqrt {870} }}{6} \le y \le \frac{{\sqrt {870} }}{6}\\
\Rightarrow GTNN:y = - \frac{{\sqrt {870} }}{6}
\end{array}$
