Làm giúp mình bài này ạ √(5 - 2√6) - √(8 - 2√15) - √(7 + 2√10) = 2√3
2 câu trả lời
#andy
\[\begin{array}{l}
\sqrt {5 - 2\sqrt 6 } - \sqrt {8 - 2\sqrt {15} } - \sqrt {7 + 2\sqrt {10} } \\
= \sqrt {2 - 2.\sqrt 2 .\sqrt 3 + 3} - \sqrt {5 - 2.\sqrt 5 .\sqrt 3 + 3} - \sqrt {5 + 2.\sqrt 5 .\sqrt 2 + 2} \\
= \sqrt {{{(\sqrt 2 - \sqrt 3 )}^2}} - \sqrt {{{(\sqrt 5 - \sqrt 3 )}^2}} - \sqrt {{{(\sqrt 5 + \sqrt 2 )}^2}} \\
= \left| {\sqrt 2 - \sqrt 3 } \right| - \left| {\sqrt 5 - \sqrt 3 } \right| - \left| {\sqrt 5 + \sqrt 2 } \right|\\
= \sqrt 3 - \sqrt 2 + \sqrt 3 - \sqrt 5 - \sqrt 5 - \sqrt 2 \\
= 2\sqrt 3 - 2\sqrt 2 - 2\sqrt 5
\end{array}\]
$\sqrt[]{5-2\sqrt[]{6}}-\sqrt[]{8-2\sqrt[]{15}}-\sqrt[]{7+2\sqrt[]{10}}$
$=\sqrt[]{2-2.\sqrt[]{2}.\sqrt[]{3}+3}-\sqrt[]{5-2.\sqrt[]{5}.\sqrt[]{3}+3}-\sqrt[]{5+2.\sqrt[]{5}.\sqrt[]{2}+2}$
$=\sqrt[]{(\sqrt[]{2}-\sqrt[]{3})²}-\sqrt[]{(\sqrt[]{5}-\sqrt[]{3})²}-\sqrt[]{(\sqrt[]{5}+\sqrt[]{2})²}$
$=|\sqrt[]{2}-\sqrt[]{3}|-|\sqrt[]{5}-\sqrt[]{3}|-|\sqrt[]{5}+\sqrt[]{2}|$
$=\sqrt[]{3}-\sqrt[]{2}+\sqrt[]{3}-\sqrt[]{5}-\sqrt[]{5}-\sqrt[]{2}$
$=2\sqrt[]{3}-2\sqrt[]{2}-2\sqrt[]{5}$