Tính: làm chi tiết giúp em `\frac{(5+2\sqrt{6})(49-20\sqrt{6})\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}`

Làm gì thì làm cứ khử mẫu cái đã sau đó giải quyết từng vẫn đề 1 là xong. 😀

`((5+2sqrt6)(49-20sqrt6)sqrt{5-2sqrt6})/(9sqrt3-11sqrt2)`

`=((5+2sqrt6)(49-20sqrt6)sqrt{5-2sqrt6}(9sqrt3+11sqrt2))/((9sqrt3)^2-(11sqrt2)^2)`

`=((5+2sqrt6)(49-20sqrt6)sqrt{5-2sqrt6}(9sqrt3+11sqrt2))/(243-242)`

`=(5+2sqrt6)(49-20sqrt6)sqrt{5-2sqrt6}(9sqrt3+11sqrt2)`

`=(5+2sqrt6)(49-20sqrt6)(9sqrt3+11sqrt2)sqrt{3-2sqrt{3.2}+2}`

`=(5+2sqrt6)(49-20sqrt6)(9sqrt3+11sqrt2)sqrt{(sqrt3-sqrt2)^2}`

`=(3+2sqrt6+2)(49-20sqrt6)(9sqrt3+11sqrt2)|sqrt3-sqrt2|`

`=(sqrt3+sqrt2)^2(49-20sqrt6)(9sqrt3+11sqrt2)(sqrt3-sqrt2)`

`=(sqrt3+sqrt2)(sqrt3-sqrt2)(sqrt3+sqrt2)(49-20sqrt6)(9sqrt3+11sqrt2)`

`=(3-2)(sqrt3+sqrt2)(49-20sqrt6)(9sqrt3+11sqrt2)`

`=(sqrt3+sqrt2)(9sqrt3+11sqrt2)(49-20sqrt6)`

`=(9.3+9sqrt6+11sqrt6+11.2)(49-20sqrt6)`

`=(27+22+20sqrt6)(49-20sqrt6)`

`=(49+20sqrt6)(49-20-sqrt6)`

`=49^2-(20sqrt6)^2`

`=2401-2400=1`.Đây số có đẹp không nào? :3