Question

tính giá trị của biểu thức

\(\frac{1}{\sqrt{10}+\sqrt{15}+\sqrt{14}+\sqrt{21}}\)

Answer 1

Ta có : \(\frac{1}{\sqrt{10}+\sqrt{15}+\sqrt{14}+\sqrt{21}}=\frac{1}{\sqrt{5}\left(\sqrt{2}+\sqrt{3}\right)+\sqrt{7}\left(\sqrt{2}+\sqrt{3}\right)}=\frac{1}{\left(\sqrt{5}+\sqrt{7}\right)\left(\sqrt{2}+\sqrt{3}\right)}\)

Answer 2

\(\frac{1}{\sqrt{10}+\sqrt{15}+\sqrt{14}+\sqrt{21}}\\ =\frac{1}{\sqrt{5}\left(\sqrt{2}+\sqrt{3}\right)+\sqrt{7}\left(\sqrt{2}+\sqrt{3}\right)}\\ =\frac{1}{\left(\sqrt{5}+\sqrt{7}\right)\left(\sqrt{2}+\sqrt{3}\right)}\)