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Violympic toán 9
Các câu hỏi tương tự
cho a,b,c >0
cmr: \(\sum\dfrac{a+b}{bc+a^2}\le\sum\dfrac{1}{a}\)
\(Cho\) \(a;b;c>0\). CMR:
\(\sum a\left(b+c\right)^2\le\dfrac{4}{9}\left(a+b+c\right)^3\)
Cho a, b, c > 0 thoã mãn: ab + bc + ca = 3. CMR: \(\dfrac{1}{1+a^2\left(b+c\right)}+\dfrac{1}{1+b^2\left(c+a\right)}+\dfrac{1}{1+c^2\left(a+b\right)}\le\dfrac{3}{abc}\)
Với mọi a,b,c . CMR
\(-\dfrac{1}{2}\le\dfrac{\left(a+b\right)\left(1-ab\right)}{\left(a^2+1\right)\left(b^2+1\right)}\le\dfrac{1}{2}\)
Cho \(0\le a\le b\le c\le1\). Tìm max
\(A=\left(a+b+c+3\right)\left(\dfrac{1}{a+1}+\dfrac{1}{b+1}+\dfrac{1}{c+1}\right)\)
cho \(a,b,c>0\),\(abc=1\)
chứng minh rằng:
\(\sum\dfrac{1}{a^4\left(b+c\right)^2}\ge\dfrac{3}{4}\)
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:\(\dfrac{1}{1+x^2}+\dfrac{1}{1+y^2}\ge\dfrac{2}{1+xy}\)
cho a,b,c>0. CMR
\(\sum\dfrac{1}{a+ab}\ge\dfrac{3}{abc+1}\)
Cho a,b,c>0 CMR :
\(\dfrac{ab}{a+b}+\dfrac{bc}{b+c}+\dfrac{ac}{a+c}\le\dfrac{a+b+c}{2}\)