Câu hỏi của manh

Question

a : $\sqrt{\left(2\sqrt{2}-1\right)^2}-\sqrt{17+12\sqrt{2}}$b : $\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}$c : $\sqrt{\left(4-3\sqrt{2}\right)^2}-\sqrt{19+6\sqrt{2}}$

⭐Hannie⭐ · Accepted Answer

$\sqrt{\left(2\sqrt{2-1}\right)^2}-\sqrt{17+12\sqrt{2}}\
=\left|2\sqrt{2}-1\right|-\sqrt{9+2\cdot3\cdot2\sqrt{2}+\left(2\sqrt{2}\right)^2}\
=2\sqrt{2}-1-\sqrt{\left(3+2\sqrt{2}\right)^2}\=2\sqrt{2}-1-\left(3+2\sqrt{2}\right)\
=2\sqrt{2}-1-3-2\sqrt{2}\
=-4$__$\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}\
=\left|2-\sqrt{5}\right|+\sqrt{9-2\cdot3\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}\
=2-\sqrt{5}+\sqrt{\left(3-\sqrt{5}\right)^2}\
=2-\sqrt{5}+3-\sqrt{5}\
=5-2\sqrt{5}$__$\sqrt{\left(4-3\sqrt{2}\right)^2}-\sqrt{19+6\sqrt{2}}\
=\left|4-3\sqrt{2}\right|-\sqrt{18+2\cdot3\cdot\sqrt{2}+1}\
=4-3\sqrt{2}-\sqrt{\left(3\sqrt{2}+1\right)^2}\
=4-3\sqrt{2}-3\sqrt{2}-1\
=3-6\sqrt{2}$Câu trả lời: $\sqrt{\left(2\sqrt{2-1}\right)^2}-\sqrt{17+12\sqrt{2}}\
=\left|2\sqrt{2}-1\right|-\sqrt{9+2\cdot3\cdot2\sqrt{2}+\left(2\sqrt{2}\right)^2}\
=2\sqrt{2}-1-\sqrt{\left(3+2\sqrt{2}\right)^2}\=2\sqrt{2}-1-\left(3+2\sqrt{2}\right)\
=2\sqrt{2}-1-3-2\sqrt{2}\
=-4$__$\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}\
=\left|2-\sqrt{5}\right|+\sqrt{9-2\cdot3\cdot\sqrt{5}+\left(\sqrt{5}\right)^2}\
=2-\sqrt{5}+\sqrt{\left(3-\sqrt{5}\right)^2}\
=2-\sqrt{5}+3-\sqrt{5}\
=5-2\sqrt{5}$__$\sqrt{\left(4-3\sqrt{2}\right)^2}-\sqrt{19+6\sqrt{2}}\
=\left|4-3\sqrt{2}\right|-\sqrt{18+2\cdot3\cdot\sqrt{2}+1}\
=4-3\sqrt{2}-\sqrt{\left(3\sqrt{2}+1\right)^2}\
=4-3\sqrt{2}-3\sqrt{2}-1\
=3-6\sqrt{2}$

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