Các câu hỏi tương tự
Cho a,b,c>0 Cmr: Nếu \(\sqrt{1+b}+\sqrt{1+c}=2\sqrt{1+a}\)thì \(b+c\ge2a\)
1. \(3x^2+21x+18+2\sqrt{x^2+7x+7}=2\)
2. \(x^4+2x^3+x^2-2+2\sqrt{x^2+2x+2}=0\)
3. Cho các số dương a,b,c CMR
\(\frac{7}{a}+\frac{5}{b}+\frac{4}{c}\ge4\left(\frac{4}{a+b}+\frac{1}{b+c}+\frac{3}{c+a}\right)\)
4. Cho \(\sqrt{1+x}+\sqrt{1+y}=2\sqrt{1+a}\)CMR \(x+y\ge2a\)
Chứng minh rằng : Nếu \(\sqrt{b+1}+\sqrt{c+1}=2\sqrt{a+1}\) thì \(b+c\ge2a\).
Mn giup mk nha.Cam on mn
Cho a,b,c >0 .Cm :a)\(\sqrt{c\left(a-c\right)}+\sqrt{c\left(b-c\right)}-\sqrt{ab}\le0\)vs a>c,b>c
b) Nếu \(\sqrt{1+b}+\sqrt{1+c}\ge2\sqrt{1+a}\)thì \(b+c\ge2a\)
Cho \(\sqrt{1+x}+\sqrt{1+y}=2\sqrt{1+a}\)
CMR:\(x+y\ge2a\)
giúp mình với!!!! Gấp nha!!!!
1, Chứng minh rằng: nếu \(\sqrt{b+1}+\sqrt{c+1}=2\sqrt{a+1}\) thì \(b+c\ge2a\)
2, Tính: \(A=\frac{1+2x}{1+\sqrt{1+2x}}-\frac{1-2x}{1-\sqrt{1-2x}}\) tại \(x=\frac{\sqrt{3}}{4}\)
Cho các số thực dương a+b+c=\(\sqrt{a}+\sqrt{b}+\sqrt{c}=2\\\).CMR
\(\dfrac{\sqrt{a}}{1+a}+\dfrac{\sqrt{b}}{1+b}+\dfrac{\sqrt{c}}{1+c}=\dfrac{2}{\sqrt{\left(1+a\right)\left(1+b\right)\left(1+c\right)}}\)
Cho a,b,c >0 CMR \(\sqrt{1+a^2}+\sqrt{1+b^2}+\sqrt{1+c^2}>=\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a}\)
Cho \(\left(\sqrt{a+1}-\sqrt{a}\right)+\left(\sqrt{b+2}-\sqrt{b+1}\right)=\left(\sqrt{c+2}-\sqrt{c+1}\right)+\left(\sqrt{c+1}-\sqrt{c}\right)\)
CMR:
\(\frac{1}{\sqrt{a+1}+\sqrt{a}}+\frac{1}{\sqrt{b+2}+\sqrt{b+1}}=\frac{1}{\sqrt{c+2}+\sqrt{c+1}}+\frac{1}{\sqrt{c+1}+\sqrt{c}}\)