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Tính: $\frac{1}{3 + \sqrt{5}} - \frac{1}{3 - \sqrt{5}} + \sqrt{20}$

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Biết Tuốt
$\begin{array}{l} \dfrac{1}{{3 + \sqrt 5 }} - \dfrac{1}{{3 - \sqrt 5 }} + \sqrt {20} \\ = \dfrac{{3 - \sqrt 5 }}{{\left( {3 + \sqrt 5 } \right)\left( {3 - \sqrt 5 } \right)}} - \dfrac{{3 + \sqrt 5 }}{{\left( {3 - \sqrt 5 } \right)\left( {3 + \sqrt 5 } \right)}} + 2\sqrt 5 \\ = \dfrac{{3 - \sqrt 5 }}{4} - \dfrac{{3 + \sqrt 5 }}{4} + 2\sqrt 5 \\ = \dfrac{{3 - \sqrt 5 - 3 - \sqrt 5 }}{4} + 2\sqrt 5 \\ = \dfrac{{ - 2\sqrt 5 }}{4} + 2\sqrt 5 \\ = \dfrac{{ - \sqrt 5 }}{2} + 2\sqrt 5 \\ = \dfrac{{3\sqrt 5 }}{2} \end{array}$
0 Trả lời 02/11/22