Question

Tính: A=\(\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}\)

Answer 1

\(2.A=\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)

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

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

= 2

Answer 2

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

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

A=\(\left|\frac{\sqrt{3}+1}{2}\right|-\left|\frac{\sqrt{3}-1}{2}\right|\)

A=\(\frac{\sqrt{3}+1-\sqrt{3}+1}{2}\)

A=\(\frac{2}{2}=1\)

Answer 3

Đấy là 2A, còn tính A nx