a.
\(x=49\Rightarrow M=\dfrac{49+7}{\sqrt{49}-5}=28\)
b.
\(N=\dfrac{\sqrt{x}\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}+\dfrac{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}-\dfrac{2x-3\sqrt{x}-15}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)
\(=\dfrac{x-5\sqrt{x}+2x+7\sqrt{x}-15-2x+3\sqrt{x}+15}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)
\(=\dfrac{x+5\sqrt{x}}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}=\dfrac{\sqrt{x}\left(\sqrt{x}+5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}-5}\)
c.
\(P=\dfrac{x+7}{\sqrt{x}-5}:\dfrac{\sqrt{x}}{\sqrt{x}-5}=\dfrac{x+7}{\sqrt{x}}=\sqrt{x}+\dfrac{7}{\sqrt{x}}\ge2\sqrt{\dfrac{7\sqrt{x}}{\sqrt{x}}}=2\sqrt{7}\)
Dấu "=" xảy ra khi \(\sqrt{x}=\dfrac{7}{\sqrt{x}}\Rightarrow x=7\)
