Question

Tính

\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

Answer 1

\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

\(=\left(\sqrt{6}+\sqrt{3}+\sqrt{2}+1\right)\left(5\sqrt{6}-4\sqrt{3}-3\sqrt{2}+5-2\sqrt{2}-\sqrt{3}\right)\)

\(=\left(\sqrt{6}+\sqrt{3}+\sqrt{2}+1\right)\left(5\sqrt{6}-5\sqrt{3}-5\sqrt{2}+5\right)\)

\(=5\left(\sqrt{6}+\sqrt{3}+\sqrt{2}+1\right)\left(\sqrt{6}-\sqrt{3}-\sqrt{2}+1\right)\)

\(=5\left[\left(\sqrt{6}+1\right)^2-\left(\sqrt{3}+\sqrt{2}\right)^2\right]\)

\(=5.\left(6+1+2\sqrt{6}-3-2\sqrt{6}\right)\)

\(=5.2=10\)

Chúc bạn học tốt và nhớ click cho mình với nhá!