1,Giải bpt sau:
a, x2 - 2x - 1 < 0
b, 2x2 - 6x + 5 > 0\(\)
2, Cho A=(\(\frac{x+2}{x\sqrt{x}-1}\)\(+\frac{\sqrt{x}}{x+\sqrt{x}+1}\)\(+\frac{1}{1-\sqrt{x}}\)) \(\div\frac{\sqrt{x}-1}{2}\)
a,Rút gọn A
b,CM 0 < A < 2
GIẢI GIÚP MÌNH NHA,CHIỀU NAY MÌNH PHẢI NỘP RỒI !!!!
a/ \(x^2-2x-1< 0\)
\(\Leftrightarrow\left(x-1\right)^2< 2\)
\(\Leftrightarrow-\sqrt{2}< x-1< \sqrt{2}\)
\(\Leftrightarrow1-\sqrt{2}< x< 1+\sqrt{2}\)
b/ \(2x^2-6x+5=\left(2x^2-\frac{2.\sqrt{2}.x.3}{\sqrt{2}}+\frac{9}{2}\right)+\frac{1}{2}=\left(\sqrt{2}x-\frac{3}{\sqrt{2}}\right)^2+\frac{1}{2}>0\)
Câu 2 tự làm nhé.
\(x^2-2x-1< 0\)
\(\left(x-2\right)x-1< 0\)
\(\left(x-2\right)x\le1\)
\(\Leftrightarrow1-\sqrt{2}< x< 1+\sqrt{2}\)