Đáp án:
a+b=6
Giải thích các bước giải:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to - 2} \frac{{5 - 2x - 9}}{{\left( {ax + b} \right)\left( {\sqrt {5 - 2x} + 3} \right)}}\\
= \mathop {\lim }\limits_{x \to - 2} \frac{{ - 4 - 2x}}{{\left( {ax + b} \right)\left( {\sqrt {5 - 2x} + 3} \right)}}\\
= \mathop {\lim }\limits_{x \to - 2} \frac{{ - 2\left( {2 + x} \right)}}{{\left( {ax + b} \right)\left( {\sqrt {5 - 2x} + 3} \right)}} = \frac{{ - 1}}{3}\\
\to \left\{ \begin{array}{l}
a.\left( { - 2} \right) + b = 0\\
\frac{{ - 2\left( {2 - 2} \right)}}{{\left( { - 2a + b} \right)\left( {\sqrt {5 - 2\left( { - 2} \right)} + 3} \right)}} = \frac{{ - 1}}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
b = 2a\\
\frac{{ - 2\left( {2 - 2} \right)}}{{\left( { - 2a + 2a} \right)\left( {\sqrt {5 - 2.\left( { - 2} \right)} + 3} \right)}} = - \frac{1}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
b = 2a\\
\frac{{ - 2\left( {2 - 2} \right)}}{{ - 2\left( {a - a} \right).6}} = - \frac{1}{3}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
b = 2a\\
a = 2
\end{array} \right. \to b = 4\\
\to a + b = 6
\end{array}\)
