Question

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 !!!! 

Answer 1

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.

Answer 2

\(x^2-2x-1< 0\)

\(\left(x-2\right)x-1< 0\)

\(\left(x-2\right)x\le1\)

\(\Leftrightarrow1-\sqrt{2}< x< 1+\sqrt{2}\)