Question

Answer 1

\(F=\sqrt{\dfrac{10-2\sqrt{21}}{10+2\sqrt{21}}}+\sqrt{\dfrac{10+2\sqrt{21}}{10-2\sqrt{21}}}\\ F=\sqrt{\dfrac{\left(\sqrt{7}-\sqrt{3}\right)^2}{\left(\sqrt{7}+\sqrt{3}\right)^2}}+\sqrt{\dfrac{\left(\sqrt{7}+\sqrt{3}\right)^2}{\left(\sqrt{7}-\sqrt{3}\right)^2}}\\ F=\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}+\dfrac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\\ F=\dfrac{10-2\sqrt{21}+10+2\sqrt{21}}{\left(\sqrt{7}+\sqrt{3}\right)\left(\sqrt{7}-\sqrt{3}\right)}\\ F=\dfrac{20}{4}=5\)