Các câu hỏi tương tự
14 tháng 1 2017 lúc 21:37
cho \(a\ge0,b\ge0\)
cmr \(\frac{1}{1+a^2}+\frac{1}{1+b^2}\ge\frac{2}{1+ab}\)
cho a,b,c \(\ge0\) và \(a+b+c\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
cmr \(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge\frac{1}{ab}+\frac{1}{ac}+\frac{1}{bc}\)
Cho \(a\ge0\), \(b\ge0\). CMR: \(\frac{1}{2}\left(a+b\right)^2+\frac{1}{4}\left(a+b\right)\ge a\sqrt{b}+b\sqrt{a}\)
\(Cho\) \(a,b,c\ge0\)\(CMR\)\(\frac{1}{a^2+ab}+\frac{1}{b^2+bc}+\frac{1}{c^2+ca}\ge\frac{27}{2\left(a+b+c\right)^2}.\)
cho a,b,c,b \(\ge0.CMR\)
\(\frac{a^2}{b^5}+\frac{b^2}{c^5}+\frac{c^2}{d^5}+\frac{d^2}{a^5}\ge\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}+\frac{1}{d^3}\)
Bài 8 :Cho \(a,b,c\ge0\) và a2 + b2 + c2 = 1
CMR : \(\frac{ac}{b}+\frac{bc}{a}+\frac{ab}{c}\ge\sqrt{3}\)
CMR nếu a,b,c \(\ge0\) thỏa mãn ab+bc+ca=3 thì \(\frac{1}{abc}+\frac{4}{\left(a+b\right)\left(b+c\right)\left(c+a\right)}\ge\frac{3}{2}\)
b1 sử dụng HDT hoặc co-sia)cho xge0,yge1,zge2cmr xsqrt{y-1}+ysqrt{x-1}le xyb)cho xge0,yge1,zge2cmrsqrt{x}+sqrt{y-1}+sqrt{z-2}lefrac{1}{2}left(x+y+zright)c)cho a,b,cge0cmr frac{1}{a}+frac{1}{b}+frac{1}{c}gefrac{1}{sqrt{ab}}+frac{1}{sqrt{bc}}+frac{1}{sqrt{ca}}
Đọc tiếp
b1 sử dụng HDT hoặc co-si
a)cho x\(\ge\)0,y\(\ge\)1,z\(\ge\)2cmr \(x\sqrt{y-1}+y\sqrt{x-1}\le xy\)
b)cho \(x\ge0,y\ge1,z\ge2cmr\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}\le\frac{1}{2}\left(x+y+z\right)\)
c)cho a,b,c\(\ge0\)cmr \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge\frac{1}{\sqrt{ab}}+\frac{1}{\sqrt{bc}}+\frac{1}{\sqrt{ca}}\)
\(CMR:\sqrt[3]{\frac{a^3+b^3}{2}}\ge\sqrt{\frac{a^2+b^2}{2}};a\ge0;b\ge0\)
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