Question

[ミ★кнôиɢ ¢ó ɢì★彡]

Tính giá trị biểu thức

Answer 1

[Đoàn Đức Hà]

\(A=\sqrt{6+3\sqrt{3}}-\sqrt{14-3\sqrt{3}}-2\sqrt{2}\)

\(A\sqrt{2}=\sqrt{12+6\sqrt{3}}-\sqrt{28-6\sqrt{3}}-4\)

\(=\sqrt{9+2.3.\sqrt{3}+3}-\sqrt{27-2.3\sqrt{3}.1+1}-4\)

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

\(=3+\sqrt{3}-3\sqrt{3}+1-4\)

\(=-2\sqrt{3}\)

Suy ra \(A=-\sqrt{6}\).