nhầm đề : \(\sqrt[4]{x+8}+\sqrt{x+4}=\sqrt{2x+3}+\sqrt{3x}\)
\(\sqrt[4]{x+8}+\sqrt{x+4}=\sqrt{2x+3}+\sqrt{3x}\)
\(\Leftrightarrow\sqrt[4]{x+8}-\sqrt{3}+\sqrt{x+4}-\sqrt{5}=\sqrt{2x+3}-\sqrt{5}+\sqrt{3x}-\sqrt{3}\)
\(\Leftrightarrow\frac{x+8-9}{\sqrt[4]{x+8}^3+\sqrt[4]{x+8}^2\sqrt{3}+3\sqrt[4]{x+8}+\sqrt{3}^3}+\frac{x+4-5}{\sqrt{x+4}+\sqrt{5}}=\frac{2x+3-5}{\sqrt{2x+3}+\sqrt{5}}+\frac{3x-3}{\sqrt{3x}+\sqrt{3}}\)
\(\Leftrightarrow\frac{x-1}{\sqrt[4]{x+8}^3+\sqrt[4]{x+8}^2\sqrt{3}+3\sqrt[4]{x+8}+\sqrt{3}^3}+\frac{x-1}{\sqrt{x+4}+\sqrt{5}}-\frac{2\left(x-1\right)}{\sqrt{2x+3}+\sqrt{5}}-\frac{3\left(x-1\right)}{\sqrt{3x}+\sqrt{3}}=0\)
\(\Leftrightarrow\left(x-1\right)\left(\frac{1}{\sqrt[4]{x+8}^3+\sqrt[4]{x+8}^2\sqrt{3}+3\sqrt[4]{x+8}+\sqrt{3}^3}+\frac{1}{\sqrt{x+4}+\sqrt{5}}-\frac{2}{\sqrt{2x+3}+\sqrt{5}}-\frac{31}{\sqrt{3x}+\sqrt{3}}\right)=0\)
Dễ thấy : pt trong ngoặc vô nghiệm
\(\Rightarrow x-1=0\Rightarrow x=1\)
