\(a,VT=\sqrt{7+2\sqrt{10}}-\sqrt{2}\\ =\sqrt{\left(\sqrt{5}\right)^2+2.\sqrt{5}.\sqrt{2}+\left(\sqrt{2}\right)^2}-\sqrt{2}\\ =\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}-\sqrt{2}\\ =\left|\sqrt{5}+\sqrt{2}\right|-\sqrt{2}\\ =\sqrt{5}+\sqrt{2}-\sqrt{2}\\ =\sqrt{5}=VP\)
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\(c,VT=\sqrt{5+\sqrt{21}}-\sqrt{5-\sqrt{21}}\\ =\dfrac{\sqrt{2}.\sqrt{5+\sqrt{21}}}{\sqrt{2}}-\dfrac{\sqrt{2}.\sqrt{5-\sqrt{21}}}{\sqrt{2}}\\ =\dfrac{\sqrt{10+2\sqrt{21}}-\sqrt{10-2\sqrt{21}}}{\sqrt{2}}\\ =\dfrac{\sqrt{\left(\sqrt{7}\right)^2+2\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2}}{\sqrt{2}}\\ =\dfrac{\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}}{\sqrt{2}}\\ =\dfrac{\sqrt{7}+\sqrt{3}-\sqrt{7}+\sqrt{3}}{\sqrt{2}}\\ =\dfrac{2\sqrt{3}}{\sqrt{2}}\\ =\sqrt{2}.\sqrt{3}\\ =\sqrt{6}=VP\)
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