Question

Chứng minh\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}=1}\)

Answer 1

có: \(VT=\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}\\ \Rightarrow VT=\left(2-\sqrt{3}\right)\sqrt{4+2.2.\sqrt{3}+3}\\ \Rightarrow VT=\left(2-\sqrt{3}\right)\sqrt{\left(2+\sqrt{3}\right)^2}\\ \Rightarrow VT=\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)\\ \Rightarrow VT=4-3=1\\ \Leftrightarrow VT=VP\left(ĐPCM\right)\)

Answer 2

\(=\left(2-\sqrt{3}\right)\cdot\sqrt{3+2\cdot2\sqrt{3}+4}\)

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

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