1. cho a,b không âm. c/m rằng:

a) nếu a < b => \(\sqrt{a}< \sqrt{b}\)

b) nếu \(\sqrt{a}< \sqrt{b}\)=> a < b

2. cho m > 0, c/m:

a) nếu m > 1 thì \(\sqrt{m}>1\) 

b) nếu m < 1 thì \(\sqrt{m}< 1\)

cho Q\(=\)(\(\frac{\sqrt{a}+3}{a+2\sqrt{a}+1}\)- \(\frac{\sqrt{a}-2}{a-1}\)).\(\frac{\sqrt{a}+1}{\sqrt{a}}\)

chứng minh \(\forall\)a sao cho a<a<1 thì Q<0

1) Cho biểu thức A = \(\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x\sqrt{x}+1}+\dfrac{1}{1-\sqrt{x}}\right)\): \(\dfrac{\sqrt{x}-1}{2}\)

a) Rút gọn A

b) C/m 0<A<2

Rút gọn:

a) \(\sqrt{\dfrac{9x^2}{25}}\) + \(\dfrac{1}{5}x\) (x<0).

b) 2xy . \(\sqrt{\dfrac{9x^2}{y^6}}-\sqrt{\dfrac{49x^2}{y^2}}\) (x<0; y>0).

c) \(\dfrac{1}{a-b}.\sqrt{a^6.\left(a-b\right)^2}\) (a<b<0).

a)Cho 0 < c ; c < b ; b < a . CMR:\(\sqrt{c\left(a-c\right)}+\sqrt{b\left(b-c\right)}\le\sqrt{ab}\)

b)Cho \(x\ge1;y\ge1\). CMR:\(\dfrac{1}{1+x^2}+\dfrac{1}{1+y^2}\ge\dfrac{2}{1+xy}\)

1.tính giá trị biểu thức \(A=\frac{1-ax}{1+ã}\sqrt{\frac{1+bx}{1-bx}}\)với \(x=\frac{1}{a}\sqrt{\frac{2a}{b}-1}\left(0< a< b< 2a\right)\)

2. cho \(M=\sqrt{\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{x^2+\sqrt{x}}{x-\sqrt{x}+1}+x+1}\).rút gọn M vs \(0\le x\le1\)

(\(\frac{\sqrt{1+a}}{\sqrt{1+a}-\sqrt{1-a}}\)+\(\frac{1-a}{\sqrt{1-a^2}-1+a}\)) (\(\sqrt{\frac{1}{a^2}}\)-1-\(\frac{1}{a}\))
điều kiện: 0<a<1