Question

[NGUYEN THI DIEP]

Cho biểu thức P=(\(\dfrac{a-3\sqrt{a}+2}{3a-7\sqrt{a}+2}\)-\(\dfrac{\sqrt{a}-3}{3a-8\sqrt{a}-3}\)+\(\dfrac{8\sqrt{a}}{9a-1}\)) : (1-\(\dfrac{2\sqrt{a}-a+1}{3\sqrt{a}+1}\))

Tìm giá trị nghuyên lớn nhất của a để P> \(\dfrac{3}{|1-3\sqrt{5}|}\)

Giup mk vs

Answer 1

[nguyen ngoc song thuy]

DAT P = Q:R \(Q=\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(3\sqrt{a}-1\right)}-\dfrac{\sqrt{a}-3}{\left(\sqrt{a}-3\right)\left(3\sqrt{a}-1\right)}+\dfrac{8\sqrt{a}}{\left(3\sqrt{a}-1\right)\left(3\sqrt{a}+1\right)}\)

\(=\dfrac{\sqrt{a}-1}{3\sqrt{a}-1}-\dfrac{1}{3\sqrt{a}+1}+\dfrac{8\sqrt{a}}{\left(3\sqrt{a}-1\right)\left(3\sqrt{a}+1\right)}\)

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

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

\(\Rightarrow P=Q:R=\dfrac{3\sqrt{a}\left(\sqrt{a}+1\right)}{\left(3\sqrt{a}-1\right)\left(3\sqrt{a}+1\right)}\times\dfrac{3\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}+1\right)}\)

\(P=\dfrac{3}{3\sqrt{a}-1}\)

\(P>\dfrac{3}{\left|1-3\sqrt{5}\right|}\Leftrightarrow\dfrac{3}{3\sqrt{a}-1}>\dfrac{3}{3\sqrt{5-1}}\)

\(3\sqrt{a}-1< 3\sqrt{5}-1\)

\(\Rightarrow0\le\sqrt{a}\le\sqrt{5}\)

\(a=\) 0 ;1 ;2 ;3 ;4

​a lớn nhất \(\Rightarrow a\) = 4

Answer 2

[Hương Yangg]

Bạn rút gọn được P chưa ?~!