cho P=\(\left(\dfrac{\sqrt{x}-x-3}{x-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{8\sqrt{x}}{x-1}\right)\)
a.rút gọn P
b.tìm gtnn gtln của P
c.tìm x để P=8
d.tìm x\(\in\) Z để P\(\in\)Z
e. tính P tại x=\(10-2\sqrt{21}\)
f.tìm x để P>5
g.so sánh P vs 4
a: \(P=\dfrac{-x+\sqrt{x}-3-\sqrt{x}-1}{x-1}:\dfrac{x+2\sqrt{x}+1-x+2\sqrt{x}-1-8\sqrt{x}}{x-1}\)
\(=\dfrac{-x-4}{x-1}\cdot\dfrac{x-1}{-4\sqrt{x}}\)
\(=\dfrac{x+4}{4\sqrt{x}}\)
c: Để P=8 thì \(x+4=32\sqrt{x}\)
=>\(\left[{}\begin{matrix}x=\left(16+6\sqrt{7}\right)^2\\x=\left(16-6\sqrt{7}\right)^2\end{matrix}\right.\)
e: Khi x=10-2 căn 21 thì \(P=\dfrac{10-2\sqrt{21}+4}{4\left(\sqrt{7}-\sqrt{3}\right)}=\dfrac{14-2\sqrt{21}}{4\left(\sqrt{7}-\sqrt{3}\right)}\)
\(=\dfrac{2\sqrt{7}\left(\sqrt{7}-\sqrt{3}\right)}{4\left(\sqrt{7}-\sqrt{3}\right)}=\dfrac{\sqrt{7}}{2}\)
