\(D=\dfrac{1}{\sqrt{h+2\sqrt{h-1}}}+\dfrac{1}{\sqrt{h-2\sqrt{h-1}}}\)
\(=\dfrac{1}{\sqrt{h-1+2\sqrt{h-1}+1}}+\dfrac{1}{\sqrt{h-1-2\sqrt{h-1}+1}}\)
\(=\dfrac{1}{\sqrt{\left(\sqrt{h-1}+1\right)^2}}+\dfrac{1}{\sqrt{\left(\sqrt{h-1}-1\right)^2}}\)
\(=\dfrac{1}{\sqrt{h-1}+1}+\dfrac{1}{\sqrt{h-1}-1}\)
\(=\dfrac{\sqrt{h-1}-1+\sqrt{h-1}+1}{\left(\sqrt{h-1}+1\right)\left(\sqrt{h-1}-1\right)}\)
\(=\dfrac{2\sqrt{h-1}}{\left(\sqrt{h-1}+1\right)\left(\sqrt{h-1}-1\right)}\)
Thay \(h=3\) vào biểu thức ta được :
\(\dfrac{2\sqrt{3-1}}{\left(\sqrt{3-1}+1\right)\left(\sqrt{3-1}-1\right)}=\dfrac{2\sqrt{2}}{\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)}=\dfrac{2\sqrt{2}}{1}=2\sqrt{2}\)
Chúc bạn học tốt
