Bài 1: Cho a,b,c >0 t/m: abc=1
CMR: \(\dfrac{1}{a^3+b^3+1}+\dfrac{1}{b^3+c^3+1}+\dfrac{1}{c^3+a^3+1}\le1\)
Bài 2: Cho a,b,c >0 t/m a+b+c=1
CMR: \(\dfrac{1+a}{1-a}+\dfrac{1+b}{1-b}+\dfrac{1+c}{1-c}\ge6\)
Bài 3: Cho a,b,c >0 t/m abc=1
CMR: \(\dfrac{ab}{a^4+b^4+ab}+\dfrac{bc}{b^4+c^4+bc}+\dfrac{ac}{c^4+a^4+ac}\le1\)
Cho a,b,c>0 thỏa mãn ab+bc+ac<=1
CMR: \(\dfrac{a}{\sqrt{a^2+1}}+\dfrac{b}{\sqrt{b^2+1}}+\dfrac{c}{\sqrt{c^2+1}}\le\dfrac{3}{2}\)
cho a,b,c>0 thỏa mãn a+b+c=1
cmr: \(\left(\dfrac{1}{a}-1\right)\left(\dfrac{1}{b}-1\right)\left(\dfrac{1}{c}-1\right)\ge8\)
Cho a,b,c>0 thỏa mãn a+b+c=\(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\). Chứng minh rằng:
\(\dfrac{1}{a^3+b+c}+\dfrac{1}{a+b^3+c}+\dfrac{1}{a+b+c^3}\le1\)
Cho a, b, c > 0 và \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=3\) . Tìm MAX của :
A= \(\dfrac{1}{\sqrt{a^2-ab+b^2}}+\dfrac{1}{\sqrt{b^2-bc+c^2}}+\dfrac{1}{\sqrt{c^2-ac+a^2}}\)
Cho a;b>0 và a+b\(\le1\). Tìm GTNN của
C=\(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{4}{ab}+3ab\)
cho a,b,c>0 thỏa mãn abc=1.
CMR:\(\dfrac{a}{ab+1}+\dfrac{b}{bc+1}+\dfrac{c}{ca+1}\ge\dfrac{3}{2}\)
Cho a, b, c > 0 thỏa mãn \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1\). CMR:
\(\dfrac{a^2}{a+bc}+\dfrac{b^2}{b+ac}+\dfrac{c^2}{c+ab}\ge\dfrac{a+b+c}{4}\)
1. Cho a,b >0; a+b ≤ 1
Tìm min \(N=ab+\dfrac{1}{ab}\)
2. Cho a,b,c >0 t/m: a+b+c ≥ 6
Tìm min \(P=5a+6b+7c+\dfrac{1}{a}+\dfrac{8}{b}+\dfrac{27}{c}\)
3. Cho a,b,c ∈ \(\left[-1;2\right]\) và \(a^2+b^2+c^2=6\)
\(CM:\) a+b+c ≥ 0
a,b,c>0 thỏa mãn `a^4 +b^4 +c^4 =3`. CMR \(\dfrac{a^2}{b^3+1}+\dfrac{b^2}{c^3+1}+\dfrac{c^2}{a^3+1}>=\dfrac{3}{2}\)
