Rút gọn hộ mình với $\frac{3\sqrt{2}}{1-\sqrt{2}-\sqrt{3}}$ 01/07/2021 Bởi Amaya Rút gọn hộ mình với $\frac{3\sqrt{2}}{1-\sqrt{2}-\sqrt{3}}$
$\begin{array}{l} \dfrac{{3\sqrt 2 }}{{1 – \sqrt 2 – \sqrt 3 }}\\ = \dfrac{{3\sqrt 2 }}{{\left( {1 – \sqrt 2 } \right) – \sqrt 3 }}\\ = \dfrac{{3\sqrt 2 \left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{\left( {1 – \sqrt 2 – \sqrt 3 } \right)\left( {1 – \sqrt 2 + \sqrt 3 } \right)}}\\ = \dfrac{{3\sqrt 2 \left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{{{\left( {1 – \sqrt 2 } \right)}^2} – 3}} = \dfrac{{3\sqrt 2 \left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{3 – 3 – 2\sqrt 2 }}\\ = \dfrac{{3\left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{ – 2}} = \dfrac{{3\left[ {\sqrt 2 – 1 – \sqrt 3 } \right]}}{2} \end{array}$ Bình luận
Đáp án: $\dfrac{-3+3\sqrt 2-3\sqrt 3}{2}$ Giải thích các bước giải: $\dfrac{3\sqrt 2}{1-\sqrt 2-\sqrt 3}$ $=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{(1-\sqrt 2-\sqrt 3)(1-\sqrt 2+\sqrt 3)}$ $=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{(1-\sqrt 2)^2-\sqrt 3^2}$ $=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{1-2\sqrt 2+2-3}$ $=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{(-2\sqrt 2}$ $=\dfrac{-3+3\sqrt 2-3\sqrt 3}{2}$. Bình luận
$\begin{array}{l} \dfrac{{3\sqrt 2 }}{{1 – \sqrt 2 – \sqrt 3 }}\\ = \dfrac{{3\sqrt 2 }}{{\left( {1 – \sqrt 2 } \right) – \sqrt 3 }}\\ = \dfrac{{3\sqrt 2 \left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{\left( {1 – \sqrt 2 – \sqrt 3 } \right)\left( {1 – \sqrt 2 + \sqrt 3 } \right)}}\\ = \dfrac{{3\sqrt 2 \left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{{{\left( {1 – \sqrt 2 } \right)}^2} – 3}} = \dfrac{{3\sqrt 2 \left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{3 – 3 – 2\sqrt 2 }}\\ = \dfrac{{3\left[ {\left( {1 – \sqrt 2 } \right) + \sqrt 3 } \right]}}{{ – 2}} = \dfrac{{3\left[ {\sqrt 2 – 1 – \sqrt 3 } \right]}}{2} \end{array}$
Đáp án:
$\dfrac{-3+3\sqrt 2-3\sqrt 3}{2}$
Giải thích các bước giải:
$\dfrac{3\sqrt 2}{1-\sqrt 2-\sqrt 3}$
$=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{(1-\sqrt 2-\sqrt 3)(1-\sqrt 2+\sqrt 3)}$
$=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{(1-\sqrt 2)^2-\sqrt 3^2}$
$=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{1-2\sqrt 2+2-3}$
$=\dfrac{3\sqrt 2(1-\sqrt 2+\sqrt 3)}{(-2\sqrt 2}$
$=\dfrac{-3+3\sqrt 2-3\sqrt 3}{2}$.