Question

A=\(\dfrac{3\sqrt{x}-5}{2\sqrt{x}+1}\)

tính giá trị của biểu thức P khi x=\(\dfrac{3-2\sqrt{2}}{4}\)

Answer 1

\(A=\left(3\cdot\dfrac{\sqrt{2}-1}{2}-5\right):\left(2\cdot\dfrac{\sqrt{2}-1}{2}+1\right)\)

\(=\dfrac{3\sqrt{2}-3-10}{2}\cdot\dfrac{1}{\sqrt{2}}=\dfrac{6-13\sqrt{2}}{4}\)

Answer 2

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

\(A=\dfrac{3\sqrt{\left(\dfrac{\sqrt{2}-1}{2}\right)^2}-5}{2\sqrt{\left(\dfrac{\sqrt{2}-1}{2}\right)^2}+1}=\dfrac{\dfrac{3\sqrt{2}-3}{2}-5}{\sqrt{2}-1+1}=\dfrac{3\sqrt{2}-3-10}{2}.\dfrac{1}{\sqrt{2}}=\dfrac{3\sqrt{2}-13}{2\sqrt{2}}=\dfrac{6-13\sqrt{2}}{4}\)