Đáp án:
Áp dụng hằng đẳng thức:
${a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)$
$\begin{array}{l}
a)\\
\left( {\sqrt {24 - {x^2}} + \sqrt {8 - {x^2}} } \right).\left( {\sqrt {24 - {x^2}} - \sqrt {8 - {x^2}} } \right)\\
= \left( {24 - {x^2}} \right) - \left( {8 - {x^2}} \right)\\
\Rightarrow \left( {\sqrt {24 - {x^2}} + \sqrt {8 - {x^2}} } \right).2 = 24 - {x^2} - 8 + {x^2}\\
\Rightarrow 2.\left( {\sqrt {24 - {x^2}} + \sqrt {8 - {x^2}} } \right) = 16\\
\Rightarrow \sqrt {24 - {x^2}} + \sqrt {8 - {x^2}} = 8\\
b)\\
\left( {\sqrt {25 - {x^2}} + \sqrt {15 - {x^2}} } \right).\left( {\sqrt {25 - {x^2}} - \sqrt {15 - {x^2}} } \right)\\
= 25 - {x^2} - 15 + {x^2}\\
\Rightarrow \left( {\sqrt {25 - {x^2}} + \sqrt {15 - {x^2}} } \right).2 = 10\\
\Rightarrow \left( {\sqrt {25 - {x^2}} + \sqrt {15 - {x^2}} } \right) = 5
\end{array}$
