[tex]f(x)=\frac{(x+\sqrt{5})(\sqrt{x+\sqrt{5}}-\sqrt{x})}{\sqrt{5}}+\frac{(x-\sqrt{5})(\sqrt{x+\sqrt{5}}+\sqrt{x})}{\sqrt{5}}[/tex]
[tex]=\frac{x(\sqrt{x+\sqrt{5}}+\sqrt{x-\sqrt{5}})+\sqrt{5}(\sqrt{x+\sqrt{5}}-\sqrt{x-\sqrt{5}})-2\sqrt{5x}}{\sqrt{5}}[/tex]
[tex]\Rightarrow f(3)=\frac{3(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}})+\sqrt{5}(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}})+2\sqrt{15}}{\sqrt{5}}[/tex]
Xét [tex]a=\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}} \Leftrightarrow a^2=3+\sqrt{5}+3-\sqrt{5}+2\sqrt{9-5}=10 \Rightarrow a=\sqrt{10}[/tex]
Xét [tex]b=\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}} \Leftrightarrow b^2=3+\sqrt{5}+3-\sqrt{5}-2\sqrt{9-5}=2 \Leftrightarrow b=\sqrt{2}[/tex]
Do đó: [tex]f(3)=\frac{3\sqrt{10}+\sqrt{10}-2\sqrt{15}}{\sqrt{5}}=3\sqrt{2}+\sqrt{2}-2\sqrt{3}=4\sqrt{2}-2\sqrt{3}[/tex]
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
