$\frac{1}{√5-2}$ + $\frac{1}{√5+2}$ $\frac{10}{√11 - √6}$ + $\frac{10}{√11 + √6}$

Đáp án:

$\displaystyle 2\sqrt{5} +4\sqrt{11}$

Giải thích các bước giải:

$\displaystyle \begin{array}{{>{\displaystyle}l}} \frac{1}{\sqrt{5} -2} +\frac{1}{\sqrt{5} +2} +\frac{10}{\sqrt{11} -\sqrt{6}} +\frac{10}{\sqrt{11} +\sqrt{6}}\\ =\frac{\sqrt{5} +2+\sqrt{5} -2}{\left(\sqrt{5} -2\right)\left(\sqrt{5} +2\right)} +\frac{10\left(\sqrt{11} +\sqrt{6}\right) +10\left(\sqrt{11} -\sqrt{6}\right)}{\left(\sqrt{11} -\sqrt{6}\right)\left(\sqrt{11} +\sqrt{6}\right)}\\ =\frac{2\sqrt{5}}{5-4} +\frac{20\sqrt{11}}{11-6} =2\sqrt{5} +4\sqrt{11} \end{array}$ 

`1/(\sqrt{5}-2)+1/(\sqrt{5}+2)+(10)/(\sqrt{11}-\sqrt{6})+(10)/(\sqrt{11}+\sqrt{6})`

`=(\sqrt{5}+2+\sqrt{5}-2)/((\sqrt{5}-2)(\sqrt{5}+2))+(10(\sqrt{11}+\sqrt{6}))/((\sqrt{11}-\sqrt{6})(\sqrt{11}+\sqrt{6}))+(10(\sqrt{11}-\sqrt{6}))/((\sqrt{11}+\sqrt{6}))`

`=(2\sqrt{5})/(1)+(10(\sqrt{11}+\sqrt{6}))/(5)+(10(\sqrt{11}-\sqrt{6}))/(5)`

`=2\sqrt{5}+2(\sqrt{11}+\sqrt{6})+2(\sqrt{11}-\sqrt{6})`

`=2\sqrt{5}+2\sqrt{11}+2\sqrt{6}+2\sqrt{11}-2\sqrt{6}`

`=2\sqrt{5}+4\sqrt{11}`