Question

Tính các giá trị của các biểu thức sau:

a. A= \(\dfrac{2}{\sqrt{3}+1}+\dfrac{6}{\sqrt{3}-1}+1\)

b. B= \(\dfrac{\sqrt{\dfrac{7}{2}+\sqrt{6}}.\left(\sqrt{12}-\sqrt{2}\right)}{\sqrt{20}}\)

Answer 1

a) \(A=\dfrac{2}{\sqrt{3}+1}+\dfrac{6}{\sqrt{3}-1}+1\)

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

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

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

\(=\dfrac{8\sqrt{3}+6}{2}\)

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

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

Answer 2

b: \(B=\dfrac{\sqrt{\dfrac{7+2\sqrt{6}}{2}\cdot2}\cdot\left(\sqrt{6}-1\right)}{2\sqrt{5}}\)

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

Answer 3

a,=\(4\sqrt{3}+3\)

b,=\(\dfrac{\sqrt{5}}{2}\)