Toán Tính: A = căn (3 – căn 5) + (3 + căn 5). 05/10/2021 By Josie Tính: A = căn (3 – căn 5) + (3 + căn 5).
\[\begin{array}{l} A = \sqrt {3 – \sqrt 5 } + \sqrt {3 + \sqrt 5 } \\ \Rightarrow \sqrt 2 A = \sqrt {2\left( {3 – \sqrt 5 } \right)} + \sqrt {2\left( {3 + \sqrt 5 } \right)} \\ \Leftrightarrow \sqrt 2 A = \sqrt {6 – 2\sqrt 5 } + \sqrt {6 + 2\sqrt 5 } \\ \Leftrightarrow \sqrt 2 A = \sqrt {{{\left( {\sqrt 5 – 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} \\ \Leftrightarrow \sqrt 2 A = \left| {\sqrt 5 – 1} \right| + \left| {\sqrt 5 + 1} \right|\\ \Leftrightarrow \sqrt 2 A = \sqrt 5 – 1 + \sqrt 5 + 1\,\,\,\left( {do\,\,\sqrt 5 – 1 > 0} \right)\\ \Leftrightarrow \sqrt 2 A = 2\sqrt 5 \\ \Leftrightarrow A = \frac{{2\sqrt 5 }}{{\sqrt 2 }} = \sqrt {10} . \end{array}\] Trả lời
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\[\begin{array}{l}
A = \sqrt {3 – \sqrt 5 } + \sqrt {3 + \sqrt 5 } \\
\Rightarrow \sqrt 2 A = \sqrt {2\left( {3 – \sqrt 5 } \right)} + \sqrt {2\left( {3 + \sqrt 5 } \right)} \\
\Leftrightarrow \sqrt 2 A = \sqrt {6 – 2\sqrt 5 } + \sqrt {6 + 2\sqrt 5 } \\
\Leftrightarrow \sqrt 2 A = \sqrt {{{\left( {\sqrt 5 – 1} \right)}^2}} + \sqrt {{{\left( {\sqrt 5 + 1} \right)}^2}} \\
\Leftrightarrow \sqrt 2 A = \left| {\sqrt 5 – 1} \right| + \left| {\sqrt 5 + 1} \right|\\
\Leftrightarrow \sqrt 2 A = \sqrt 5 – 1 + \sqrt 5 + 1\,\,\,\left( {do\,\,\sqrt 5 – 1 > 0} \right)\\
\Leftrightarrow \sqrt 2 A = 2\sqrt 5 \\
\Leftrightarrow A = \frac{{2\sqrt 5 }}{{\sqrt 2 }} = \sqrt {10} .
\end{array}\]