Cho: \(\left(a+b+c\right)^2=a^2+b^2+c^2\) và a, b, c khác 0. CMR: \(\dfrac{1}{a^3}+\dfrac{1}{b^3}+\dfrac{1}{c^3}=\dfrac{3}{abc}\)
Cho: \(\left(a+b+c\right)^2=a^2+b^2+c^2\) và a,b, c khác 0. CMR: \(\dfrac{1}{a^3}+\dfrac{1}{b^3}+\dfrac{1}{c^3}=\dfrac{3}{abc}\)
Cho a,b,c>0 và a2+b2+c2 =3
CMR \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{3}{2}\left(a+b+c\right)\) ≥ 15/2
Cho biết: \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=2\); \(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}=2\). CMR: a+b+c=abc
Bài 1: Cho a,b,c là những số dương thỏa mãn: a+b+c=3
CMR: \(\dfrac{a^2}{a+2b^3}+\dfrac{b^2}{b+2c^3}+\dfrac{c^2}{c+2a^3}\ge1\)
Bài 2: Cho a, b, c thỏa mãn: ab+bc+ca=3
CMR: \(\dfrac{a}{2b^3+1}+\dfrac{b}{2c^3+1}+\dfrac{c}{2a^3+1}\ge1\)
Bài 3: Cho a, b, c > 0. CMR: \(\dfrac{a^2}{b}+\dfrac{b^2}{c}+\dfrac{c^2}{a}\ge a+3b\)
Dấu = xảy ra khi a=b=2c
Cho a,b,c > 0 . CMR :
a) \(\dfrac{a}{b^2}+\dfrac{b}{c^2}+\dfrac{c}{a^2}\) ≥ \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)
Bài 1: a, b, c là 3 cạnh của tam giác. CMR:
\(\dfrac{a^2}{b+c-a}+\dfrac{b^2}{c+a-b}+\dfrac{c^2}{a+b-c}\ge a+b+c\)
Bài 2: a, b là số dương. CMR:
\(ab+\dfrac{a}{b}+\dfrac{b}{a}\ge a+b+1\)
Bài 3: a,b,c>0 thỏa mãn: (a+c)(b+c)=1. CMR:
\(\dfrac{1}{\left(a-b\right)^2}+\dfrac{1}{\left(a+c\right)^2}+\dfrac{1}{\left(b+c\right)^2}\ge4\)
Cho \(a;b;c>0\). CMR:
\(\dfrac{a+b}{a^2+bc}+\dfrac{b+c}{b^2+ca}+\dfrac{c+a}{c^2+ab}\le\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)
Cho: \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\) và a, b, c \(\ne\) 0
\(A=\dfrac{b^2c^2}{a}+\dfrac{c^2a^2}{b}+\dfrac{a^2b^2}{c}\)
CMR: 3abc = A
