Question

cho mình hỏi cách giải bài này với

 

\[ \frac{13}{\sqrt{20} - \sqrt{7}} + \frac{1}{2 - \sqrt{5}} + \frac{2\sqrt{7} - 7}{\sqrt{7}} \]

Answer 1

`13/(\sqrt{20}-\sqrt{7})+1/(2-\sqrt{5})+(2\sqrt{7}-7)/(\sqrt{7})`

`= (13(\sqrt{20}+\sqrt{7}))/((\sqrt{20}-\sqrt{7})(\sqrt{20}+\sqrt{7})) + (2+\sqrt{5})/((2-\sqrt{5})(2+\sqrt{5}))+(\sqrt{7}(2-\sqrt{7}))/(\sqrt{7})`

`= (13(\sqrt{20}+\sqrt{7}))/((\sqrt{20})^2-(\sqrt{7})^2) + (2+\sqrt{5})/(2^2-(\sqrt{5})^2)+2-\sqrt{7}`

`= (13(\sqrt{20}+\sqrt{7}))/(20-7)+(2+\sqrt{5})/(4-5)+2-\sqrt{7}`

`= (13(\sqrt{20}+\sqrt{7}))/13+(2+\sqrt{5})/(-1)+2-\sqrt{7}`

`= \sqrt{2^2 .5}+\sqrt{7} - (2+\sqrt{5})+2-\sqrt{7}`

`=  2\sqrt{5}+\sqrt{7} - 2-\sqrt{5}+2-\sqrt{7}`

`= \sqrt{5}`