Question

[MẠNH Trần Đinh]

4\(\frac{4}{\sqrt{3-1}}+\frac{5}{3-\sqrt{2}}-2\sqrt{3}\)

Answer 1

[KAl(SO4)2·12H2O]

\(\frac{4}{\sqrt{3-1}}+\frac{5}{3-\sqrt{2}}-2\sqrt{3}\)

\(=2\sqrt{3}+\frac{5}{3-\sqrt{2}}-2\sqrt{3}\)

\(=2\sqrt{2}+\frac{5\left(3+\sqrt{2}\right)}{7}-2\sqrt{3}\)

Answer 2

[Vy Thị Hoàng Lan ( Toán Học )]

\(4\frac{4}{\sqrt{3-1}}+\frac{5}{3-\sqrt{2}}-2\sqrt{3}\)

\(=4\frac{4}{\sqrt{2}}+\frac{5}{3-\sqrt{2}}-2\sqrt{3}\)

\(=4+2\sqrt{2}+\frac{5}{3-\sqrt{2}}-2\sqrt{3}\)

\(=\frac{\left(4+2\sqrt{2}\right)\left(3-\sqrt{2}\right)+5-2\sqrt{3}\left(3-\sqrt{2}\right)}{3-\sqrt{2}}\)

\(=\frac{12-4\sqrt{2}+6\sqrt{2}-4+5-6\sqrt{3}+2\sqrt{6}}{3-\sqrt{2}}\)

\(=\frac{13+2\sqrt{2}-6\sqrt{3}+2\sqrt{6}}{3-\sqrt{2}}\)

\(=\frac{\left(13+2\sqrt{2}-6\sqrt{3}+2\sqrt{6}\right)\left(3+\sqrt{2}\right)}{9-2}\)

\(=\frac{39+13\sqrt{2}+6\sqrt{2}+4-18\sqrt{3}-6\sqrt{6}+6\sqrt{6}+4\sqrt{3}}{7}\)

\(=\frac{43+19\sqrt{2}-14\sqrt{3}}{7}\)