ĐKXĐ: \(a\ge0;b\ge0;a\ne b\)
\(P=\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}-\dfrac{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+2\sqrt{b}\right)}{\sqrt{a}+2\sqrt{b}}\)
\(=\sqrt{a}+\sqrt{b}-\left(\sqrt{a}-\sqrt{b}\right)\)
\(=2\sqrt{b}\)
Do \(\sqrt{b}\ge0;\forall b\ge0\Rightarrow2\sqrt{b}\ge0\Rightarrow P\ge0\)
\(\left\{{}\begin{matrix}a+b=20\\P=8\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a+b=20\\2\sqrt{b}=8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a+b=20\\\sqrt{b}=4\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a+b=20\\b=16\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a=4\\b=16\end{matrix}\right.\)
