\(\left(a+b+c\right)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=26.31=806\)
\(\Rightarrow1+\frac{a}{b}+\frac{a}{c}+\frac{b}{a}+1+\frac{b}{c}+\frac{c}{a}+\frac{c}{b}+1=806\)
\(\Rightarrow\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{a}{c}+\frac{c}{b}+\frac{b}{a}=803\)
Cho \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}\) (abc khác 0,a+b+c khác 0).Chứng minh \(\frac{1}{a^3}+\frac{1}{b^3^{^{^{^{^{^{^{^{^{^{^{^{^{^{^{^#}}}}}}}}}}}}}}}}+\frac{1}{c^3}=\frac{1}{a^3+b^3+c^3}\)
Cho \(\frac{1}{a}-\frac{1}{b}+\frac{1}{c}=\frac{1}{a-b+c}\) và a,b,c≠0 thỏa mãn: a<b<c
CMR: \(\frac{1}{a^{2019}}-\frac{1}{b}+\frac{1}{c^{2019}}=\frac{1}{a^{2019}-b+c^{2019}}\)
Cho a,b,c > 0 . Chứng minh rằng: \(\frac{a}{\sqrt{b}}+\frac{b}{\sqrt{c}}+\frac{c}{\sqrt{a}}\ge2\left(\frac{a}{b+1}+\frac{b}{c+1}+\frac{c}{a+1}\right)\)
Cho \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=2017\) và a + b + c = 2018. Tính \(A=\frac{a+b}{c}+\frac{b+c}{a}+\frac{a+c}{b}\)
Cho a,b,c > 0 . Cm : \(\frac{a}{b^2}+\frac{b}{c^2}+\frac{c}{a^2}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
cho a,b,c>0.CMR:\(\frac{a}{b^2}+\frac{b}{c^2}+\frac{c}{a^2}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
Cho 3 số thực dương a, b, c.
Chứng minh rằng: \(\frac{b}{a\left(a+b\right)}+\frac{c}{b\left(b+c\right)}+\frac{a}{c\left(c+a\right)}\ge\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
a, Cho a,b>0 , CMR: \(\frac{1}{a}+\frac{1}{b}\ge\frac{4}{a+b}\)
b. Cho a,b,c,d > 0. CMR: \(\frac{a-d}{d+b}+\frac{d-b}{b+c}+\frac{b-c}{c+a}+\frac{c-a}{a+d}\ge0\)
Cho a,b,c là các số dương. CM bđt:
\(\frac{1}{2a+b+c}+\frac{1}{a+2b+c}+\frac{1}{a+b+2c}\le\frac{1}{4}+\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
