Cho a ,c > 0 và ab > 1. Chứng minh rằng : \(\dfrac{1}{1+a^4}+\dfrac{1}{1+b^4}+\dfrac{1}{1+c^4}\ge\dfrac{1}{1+ab^3}+\dfrac{1}{1+bc^3}+\dfrac{1}{ca^3}\)
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Chứng minh rằng : \(\dfrac{1}{1+a^4}+\dfrac{1}{1+b^4}+\dfrac{1}{1+c^4}\ge\dfrac{1}{1+ab^3}+\dfrac{1}{1+bc^3}+\dfrac{1}{1+ca^3}\)
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Cho a,b,c thuộc [1;2] Hãy chứng minh \(\dfrac{1}{4+a-ab}+\dfrac{1}{4+b-bc}+\dfrac{1}{4+c-ca}\ge\dfrac{3}{3+abc}\)
Cho a,b,c Là 3 cạnh tam giác . Chứng minh rằng
\(\dfrac{1}{\sqrt{ab+bc}}+\dfrac{1}{\sqrt{bc+ca}}+\dfrac{1}{\sqrt{ca+ab}}\ge\dfrac{1}{\sqrt{a^2+bc}}+\dfrac{1}{\sqrt{b^2+ac}}+\dfrac{1}{\sqrt{c^2+ab}}\)
Cho 3 số dương a, b, c thỏa mãn: ab+bc+ca=3. Chứng minh: \(\dfrac{1}{a^2+1}+\dfrac{1}{b^2+1}+\dfrac{1}{c^2+1}\ge\dfrac{3}{2}\)
Cho a, b, c > 0 thoả mãn: \(a+b+c=1\). Chứng minh: \(\dfrac{ab}{a^2+b^2}+\dfrac{bc}{b^2+c^2}+\dfrac{ca}{c^2+a^2}+\dfrac{1}{4}\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)\ge\dfrac{15}{4}\)
a, Cho a,b > 0 . CMR :\(\dfrac{1}{1+a^2}\)+ \(\dfrac{1}{1+b^2}\) \(\ge\)\(\dfrac{2}{1+ab}\) nếu ab \(\ge\)1
b, Cho a,b,c \(\ge1\). CMR : \(\dfrac{1}{1+a^4}\) + \(\dfrac{1}{1+b^4}\) + \(\dfrac{1}{1+c^4}\) \(\ge\)\(\dfrac{1}{1+ab^3}\) + \(\dfrac{1}{1+bc^3}\) + \(\dfrac{1}{1+ca^3}\)
choa a,b,c là các số thực dương thỏa mãn : a+b+c=1
chứng minh rằng : \(\dfrac{ab}{ab+c}+\dfrac{bc}{bc+a}+\dfrac{ca}{ca+b}\ge\dfrac{3}{4}\)
Cho \(a,b,c>0\) thỏa mãn \(a^4+b^4+c^4=3\). Chứng minh:
\(\dfrac{a^2}{b^3+1}+\dfrac{b^2}{c^3+1}+\dfrac{c^2}{a^3+1}\ge\dfrac{3}{2}\)
