a. ĐKXĐ: \(x\ge0;x\ne25\)
b.
\(M=\left(\dfrac{3\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}-\dfrac{2\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}+\dfrac{\sqrt{x}-21}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\right).\left(\dfrac{\sqrt{x}+5}{2}\right)\)
\(=\left(\dfrac{3\sqrt{x}+15-2\sqrt{x}+10+\sqrt{x}-21}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\right)\left(\dfrac{\sqrt{x}+5}{2}\right)\)
\(=\dfrac{2\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}.\dfrac{\left(\sqrt{x}+5\right)}{2}=\dfrac{\sqrt{x}-2}{\sqrt{x}-5}\)
c.
\(M=\dfrac{\sqrt{x}-2}{\sqrt{x}-5}=1+\dfrac{3}{\sqrt{x}-5}\)
\(M\in Z\Rightarrow\dfrac{3}{\sqrt{x}-5}\in Z\Rightarrow\sqrt{x}-5=Ư\left(3\right)\)
\(\Rightarrow\sqrt{x}-5=\left\{-3;-1;1;3\right\}\Rightarrow\sqrt{x}=\left\{2;4;6;8\right\}\)
\(\Rightarrow x=\left\{4;16;36;64\right\}\)
d.
\(x=14-6\sqrt{5}=\left(3-\sqrt{5}\right)^2\)
\(\Rightarrow M=\dfrac{\sqrt{\left(3-\sqrt{5}\right)^2}-2}{\sqrt{\left(3-\sqrt{5}\right)^2}-5}=\dfrac{1-\sqrt{5}}{-2-\sqrt{5}}=7-3\sqrt{5}\)
