Question

* Chứng minh đẳng thức:

\(\left(\dfrac{14}{\sqrt{14}}+\dfrac{\sqrt{12}+\sqrt{30}}{\sqrt{2}+\sqrt{5}}\right).\sqrt{5-\sqrt{21}}=4\)

Answer 1

\(VT=\left(\dfrac{\sqrt{14.14}}{\sqrt{14}}+\dfrac{\sqrt{6}\left(\sqrt{2}+\sqrt{5}\right)}{\sqrt{2}+\sqrt{5}}\right).\sqrt{5-\sqrt{21}}\)

\(=\left(\sqrt{14}+\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)

\(=\sqrt{30-6\sqrt{21}}+\sqrt{70-14\sqrt{21}}\)

\(=\sqrt{21-2.3\sqrt{21}+9}+\sqrt{21-2.7.\sqrt{21}+49}\)

\(=\sqrt{\left(\sqrt{21}-3\right)^2}+\sqrt{\left(7-\sqrt{21}\right)^2}\)

\(=\sqrt{21}-3+7-\sqrt{21}=4\)