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Cho a,b,c 0.Chứng minh rằnga,frac{1}{a}+frac{1}{b}+frac{1}{c}gefrac{2}{a+b}+frac{2}{b+c}+frac{2}{c+a}b,frac{4}{a}+frac{5}{b}+frac{3}{c}ge4left(frac{3}{a+b}+frac{2}{b+c}+frac{1}{c+a}right)
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Cho a,b,c > 0.Chứng minh rằng
a,\(\frac{1}{a}\)+\(\frac{1}{b}\)+\(\frac{1}{c}\)\(\ge\)\(\frac{2}{a+b}\)+\(\frac{2}{b+c}\)+\(\frac{2}{c+a}\)
b,\(\frac{4}{a}\)+\(\frac{5}{b}\)+\(\frac{3}{c}\)\(\ge\)\(4\left(\frac{3}{a+b}+\frac{2}{b+c}+\frac{1}{c+a}\right)\)
Cho a,b,c 0.Chứng minh rằnga,frac{1}{a}+frac{1}{b}+frac{1}{c}gefrac{2}{a+b}+frac{2}{b+c}+frac{2}{c+a}b,frac{4}{a}+frac{5}{b}+frac{3}{c}ge4left(frac{3}{a+b}+frac{2}{b+c}+frac{1}{c+a}right)
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Cho a,b,c > 0.Chứng minh rằng
a,\(\frac{1}{a}\)+\(\frac{1}{b}\)+\(\frac{1}{c}\)\(\ge\)\(\frac{2}{a+b}\)+\(\frac{2}{b+c}\)+\(\frac{2}{c+a}\)
b,\(\frac{4}{a}\)+\(\frac{5}{b}\)+\(\frac{3}{c}\)\(\ge\)\(4\left(\frac{3}{a+b}+\frac{2}{b+c}+\frac{1}{c+a}\right)\)
Cho a,b,c >0 thỏa mãn a+b+c\(\le\)\(\frac{3}{2}\).Chứng minh
a,\(\frac{1}{a}\)+\(\frac{1}{b}\)+\(\frac{1}{c}\)\(\ge\)6
b,a+ b+ c+ \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)\(\ge\)\(\frac{15}{2}\)
cho a, b, c>0. CMR a\(\frac{a^3}{b}\ge a^2+ab-b^2\)
CM \(\frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2}\ge\frac{c}{b}+\frac{b}{a}+\frac{a}{c}\)
Cho a, b, c là độ dài 3 cạnh của tam giác CM \(\frac{1}{a+b-c}+\frac{1}{b+c-a}+\frac{1}{c+a-b}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
Cho a, b, c > 0. CM:
a)\(\frac{a}{2a+b+c}+\frac{b}{a+2b+c}+\frac{c}{a+b+2c}\le\frac{3}{4}\)
b)\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge\frac{b+c}{a^2+bc}+\frac{c+a}{b^2+ac}+\frac{a+b}{c^2+ab}\)
c)\(\frac{a^2}{b^2+c^2}+\frac{b^2}{c^2+a^2}+\frac{c^2}{a^2+b^2}\ge\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\)
Làm được câu nào thì làm giúp mình câu đó nhé!
21 tháng 4 2019 lúc 8:45
Cho a,b,c >0 CMr :
\(a.\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+c}\ge\frac{a+b+c}{2}.\)
\(b.\frac{bc}{a}+\frac{ac}{b}+\frac{ab}{c}\ge a+b+c\)
Bài 2 : cho a, b, c> 0
1 ) \(\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+c}\ge\frac{a+b+c}{2}\)
2) \(\frac{bc}{a}+\frac{ac}{b}+\frac{ab}{c}\ge a+b+c\)
3 ) \(\frac{ab}{a+b}+\frac{bc}{b+c}+\frac{ca}{c+a}\le\frac{a+b+c}{2}\)
4) \(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c\)
Cho a, b, c > 0. CM:
a) \(\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}\ge\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+a}\)
b) \(\frac{a^2+b^2}{a+b}+\frac{b^2+c^2}{b+c}+\frac{a^2+c^2}{a+c}\le\frac{3\left(a^2+b^2+c^2\right)}{a+b+c}\)
c) \(\frac{a^2+b^2}{a^2-2ab+b^2}+\frac{b^2+c^2}{b^2-2bc+c^2}+\frac{c^2+a^2}{c^2-2ac+a^2}\ge\frac{5}{2}\)
(a, b, c đôi một khác nhau)
cho a,b,c>0. C/M a) \(\frac{_{-a+b+c}}{2a}+\frac{a-b+c}{2b}+\frac{a+b-c}{2c}\ge\frac{3}{2}\)\(\frac{3}{2}\)
b) \(\frac{a^2}{c}+\frac{b^2}{a}+\frac{c^2}{b}\ge a+b+c\)