Đáp án: $\begin{array}{l}\dfrac{{\sqrt {6 – 2\sqrt 5 } + 2}}{{\sqrt {6 – 2\sqrt 5 } – 2}} = \dfrac{{\sqrt {{{\left( {\sqrt 5 – 1} \right)}^2}} + 2}}{{\sqrt {{{\left( {\sqrt 5 – 1} \right)}^2}} – 2}}\\ = \dfrac{{\sqrt 5 – 1 + 2}}{{\sqrt 5 – 1 – 2}} = \dfrac{{\sqrt 5 + 1}}{{\sqrt 5 – 3}}\\ = \dfrac{{\left( {\sqrt 5 + 1} \right)\left( {\sqrt 5 + 3} \right)}}{{\left( {\sqrt 5 – 3} \right)\left( {\sqrt 5 + 3} \right)}}\\ = \dfrac{{5 + 3\sqrt 5 + \sqrt 5 + 3}}{{5 – 9}}\\ = \dfrac{{8 + 4\sqrt 5 }}{{ – 4}}\\ = – 2 – \sqrt 5 \end{array}$ Bình luận
Đáp án:
$\begin{array}{l}
\dfrac{{\sqrt {6 – 2\sqrt 5 } + 2}}{{\sqrt {6 – 2\sqrt 5 } – 2}} = \dfrac{{\sqrt {{{\left( {\sqrt 5 – 1} \right)}^2}} + 2}}{{\sqrt {{{\left( {\sqrt 5 – 1} \right)}^2}} – 2}}\\
= \dfrac{{\sqrt 5 – 1 + 2}}{{\sqrt 5 – 1 – 2}} = \dfrac{{\sqrt 5 + 1}}{{\sqrt 5 – 3}}\\
= \dfrac{{\left( {\sqrt 5 + 1} \right)\left( {\sqrt 5 + 3} \right)}}{{\left( {\sqrt 5 – 3} \right)\left( {\sqrt 5 + 3} \right)}}\\
= \dfrac{{5 + 3\sqrt 5 + \sqrt 5 + 3}}{{5 – 9}}\\
= \dfrac{{8 + 4\sqrt 5 }}{{ – 4}}\\
= – 2 – \sqrt 5
\end{array}$
Đáp án:
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