Ta có
\(\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}=\frac{a}{c}+\frac{b}{c}+\frac{b}{a}+\frac{c}{a}+\frac{c}{b}+\frac{a}{b}\)
\(\left(\frac{a}{c}+\frac{c}{a}\right)+\left(\frac{a}{b}+\frac{b}{a}\right)+\left(\frac{b}{c}+\frac{c}{b}\right)\)
Áp dụng cô si cho từng cặp
\(\frac{a}{c}+\frac{c}{a}\ge2;\frac{a}{b}+\frac{b}{a}\ge2;\frac{b}{c}+\frac{c}{b}\ge2\)
=>....
Dấu = xảy ra <=>a=b=c
cmr : a^2/b^2 +b^2/c^2+c^2/a^2 luon luon lon hon hoac bang c/b+ b/a+ a/c voi a,b,c lon hon 0
Cho a,b,c Cmr a+b/c + b+c/a + c+a/b > hoac = 6
cho a,b,c la 3 canh cua mot tam giac cmr
A=\(\frac{a}{b+c-a}+\frac{b}{a+c-b}+\frac{c}{a+b-c}\)
lon hon hoac bang 3
làm ơn giúp tui với
CMR so thuc a,b,c thi a^2+b^2+c^2+ab+bc+ca lon hon hoac bang 0
CMR so thuc a,b,c thi a^2+b^2+c^2+ab+bc+ca lon hon hoac bang 0
Bai 2: cho a,b,c>0.CMR
\(\frac{a^3}{bc}+\frac{b^3}{ac}+\frac{c^3}{ab}\)lon hon hoac bang a+b+c
cho a,b,c>1.cmr \(\frac{a^2}{b-1}\)+\(\frac{b^2}{c-1}\)+\(\frac{c^2}{a-1}\)lon hon hoac bang 12
cho cac so thuc duong thoa man a+b+c=3.cmr:
(a2+ab2/b2+a+b)+(b2+bc2/c2+b+c)+(c2+ca2/a2+c+a) lon hon hoac bang 2
Cho a,b,c>0.CMR
\(\frac{1}{a^3+b^{2+}abc}+\frac{1}{b^3+c^3+abc}+\frac{1}{c^3+a^3+abc}\)be hon hoac bang\(\frac{1}{abc}\)
