Cho A = \(\dfrac{b^2}{a+b}+\dfrac{c^2}{b+c}+\dfrac{a^2}{a+c}\); B= \(\dfrac{a^2}{a+b}+\dfrac{b^2}{b+c}+\dfrac{c^2}{a+c}\). CMR A = B
Cho a,b,c >0 .CMR:
\(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< \sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{a}{c+b}}+\sqrt{\dfrac{c}{a+b}}\)
Cho a,b,c >0 .CMR:
\(\dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< \sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}\)
Cho a;b;c >0.
CMR : \(\dfrac{a^2}{b^2+c^2}+\dfrac{b^2}{a^2+c^2}+\dfrac{c^2}{a^2+b^2}\ge\dfrac{a}{b+c}+\dfrac{b}{a+c}+\dfrac{c}{a+b}\)
Cho \(\dfrac{a+b-c}{c}=\dfrac{b+c-a}{a}=\dfrac{c+a-b}{b}\).Tính P =\(\left(1+\dfrac{a}{b}\right)\left(1+\dfrac{c}{b}\right)\left(1+\dfrac{a}{c}\right)\)
Cho a,b,c là 3 số khác 0 thỏa mãn \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\).CMR \(\dfrac{1}{a^3}+\dfrac{1}{b^3}+\dfrac{1}{c^3}=\dfrac{3}{abc}\)
Cho a,b,c là độ dài 3 cạnh của tam giác có p = \(\dfrac{a+b+c}{2}\)
CMR : \(\dfrac{1}{p-a}+\dfrac{1}{p-b}+\dfrac{1}{p-c}>2\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)\)
Cho \(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}=1\)
C/m \(\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}=0\)
Cho a,b,c thỏa mãn \(\dfrac{a+b-c}{c}=\dfrac{b+c-a}{a}=\dfrac{c+a-b}{b}\)
Tính giá trị M = \(\left(1+\dfrac{b}{a}\right)\left(1+\dfrac{c}{b}\right)\left(1+\dfrac{a}{c}\right)\)
