15/√6 + 1 + 4/ √ 6 -2 + 12/√ 6 -3 - √6

Đáp án:

$A = - 11$

Giải thích các bước giải:

Ta có : $A = \frac{15}{\sqrt[]{6}+1} + \frac{4}{\sqrt[]{6}-2} + \frac{12}{\sqrt[]{6}-3} - \sqrt[]{6}$

⇔ $A = \frac{15(\sqrt[]{6}-1)}{(\sqrt[]{6}+1)(\sqrt[]{6}-1)} + \frac{4(\sqrt[]{6}+2)}{(\sqrt[]{6}-2)(\sqrt[]{6}+2)} + \frac{12(\sqrt[]{6}+3)}{(\sqrt[]{6}-3)(\sqrt[]{6}+3)} - \sqrt[]{6}$

⇔ $A = \frac{15(\sqrt[]{6}-1)}{6-1} + \frac{4(\sqrt[]{6}+2)}{6-4} + \frac{12(\sqrt[]{6}+3)}{6-9} - \sqrt[]{6}$

⇔ $A = \frac{15(\sqrt[]{6}-1)}{5} + \frac{4(\sqrt[]{6}+2)}{2} + \frac{12(\sqrt[]{6}+3)}{-3} - \sqrt[]{6}$

⇔ $A = 3( \sqrt[]{6} - 1 ) + 2( \sqrt[]{6} + 2 ) - 4( \sqrt[]{6} + 3 ) - \sqrt[]{6}$

⇔ $A = 3\sqrt[]{6} - 3 + 2\sqrt[]{6} + 4 - 4\sqrt[]{6} - 12 - \sqrt[]{6}$

⇔ $A = - 11$