15/căn 6 + 1 + 4/ căn 6 -2 + 12/ căn 6 -3 - căn 6 Tính

Đáp án:

$M = - 11$

Giải thích các bước giải:

Ta có : 

$M = \frac{15}{\sqrt[]{6}+1} + \frac{4}{\sqrt[]{6}-2} + \frac{12}{\sqrt[]{6}-3} - \sqrt[]{6}$

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

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

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

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

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

⇔ $M = - 11$

Đáp án:

$-11$

Giải thích các bước giải:

$\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}+\dfrac{12}{\sqrt{6}-3}-\sqrt{6}$

$=3\left(\sqrt{6}-1\right)+2\left(\sqrt{6}+2\right)-4\left(\sqrt{6}+3\right)-\sqrt{6}$

$=3\sqrt{6}-3+2\left(\sqrt{6}+2\right)-4\left(\sqrt{6}+3\right)-\sqrt{6}$

$=3\sqrt{6}-3+2\sqrt{6}+4-4\left(\sqrt{6}+3\right)-\sqrt{6}$

$=3\sqrt{6}-3+2\sqrt{6}+4-4\sqrt{6}-12-\sqrt{6}$

$=-3+4-12$

$=-11$