\(VT=\left(\dfrac{\sqrt{14}.\sqrt{14}}{\sqrt{14}}+\dfrac{\sqrt{6}\left(\sqrt{2}+\sqrt{5}\right)}{\sqrt{2}+\sqrt{5}}\right)\sqrt{5-\sqrt{21}}\\ =\left(\sqrt{14}+\sqrt{6}\right)\sqrt{5-\sqrt{21}}\\ =\sqrt{14}.\sqrt{5-\sqrt{2}1}+\sqrt{6}.\sqrt{5-\sqrt{21}}\\ =\sqrt{70-14\sqrt{21}}+\sqrt{30-6\sqrt{21}}\\ =\sqrt{49-2.7.\sqrt{21}+21}+\sqrt{9-2.3.\sqrt{21}+21}\\ =\sqrt{\left(7-\sqrt{21}\right)^2}+\sqrt{\left(3-\sqrt{21}\right)^2}\\ =\left|7-\sqrt{21}\right|+\left|3-\sqrt{21}\right|\\ =7-\sqrt{21}+\sqrt{21}-3\\ =7-3=4=VP\)
\(VT=\left(\sqrt{14}+\sqrt{6}\right)\cdot\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{7}+\sqrt{3}\right)\cdot\sqrt{10-2\sqrt{21}}\)
=(căn 7+căn 3)(căn 7-căn 3)
=7-3
=4=VP
VT= \(\left(\sqrt{14}+\dfrac{\sqrt{6}\left(\sqrt{2}+\sqrt{5}\right)}{\sqrt{2}+\sqrt{5}}\right).\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{14}+\sqrt{6}\right).\sqrt{5-\sqrt{21}}\)
\(=\left(\sqrt{7}+\sqrt{3}\right).\sqrt{10-2\sqrt{21}}\)
\(=\left(\sqrt{7}+\sqrt{3}\right).\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}=\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)\)
\(=7-3=4\)
