Question

rút gọn A

A=\(\frac{2}{5+\sqrt{7}}+\frac{\sqrt{28}}{2}-2\)

Answer 1

\(A=\frac{2}{5+\sqrt{7}}+\frac{\sqrt{28}}{2}-2\)

\(A=\frac{2.\left(5-\sqrt{7}\right)}{25-7}+\frac{2\sqrt{7}}{2}-2\)

\(A=\frac{2.\left(5-\sqrt{7}\right)}{18}+\sqrt{7}-2\)

\(A=\frac{5-\sqrt{7}}{9}+\sqrt{7}-2\)

\(A=\frac{5-\sqrt{7}+9\sqrt{7}-18}{9}\)

\(A=\frac{-13+8\sqrt{7}}{9}\)

Vậy \(A=\frac{-13+8\sqrt{7}}{9}\)

Answer 2

\(A=\frac{2}{5+\sqrt{7}}+\frac{\sqrt{28}}{2}-2\)

\(=\frac{2\left(5-\sqrt{7}\right)}{25-7}+\frac{2\sqrt{7}}{2}-2\)

\(=\frac{2\left(5-\sqrt{7}\right)}{18}+\sqrt{7}-2\)

\(=\frac{2\left(5-\sqrt{7}\right)}{2.9}+\sqrt{7}-2=\frac{5-\sqrt{7}}{9}+\sqrt{7}-2\)

Answer 3

Bài làm:

\(A=\frac{2}{5+\sqrt{7}}+\frac{\sqrt{28}}{2}-2\)

\(A=\frac{2\left(5-\sqrt{7}\right)}{\left(5+\sqrt{7}\right)\left(5-\sqrt{7}\right)}+\frac{\sqrt{4}.\sqrt{7}}{2}-2\)

\(A=\frac{10-2\sqrt{7}}{25-7}+\sqrt{7}-2\)

\(A=\frac{5}{9}-\frac{\sqrt{7}}{9}+\sqrt{7}-2\)

\(A=\frac{5-\sqrt{7}+9\sqrt{7}-18}{9}=\frac{-13+8\sqrt{7}}{9}\)