Ta có: \(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=1\)
\(\Rightarrow\left(a+b+c\right)\left(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\right)=a+b+c\)
\(\Rightarrow\left(\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}\right)+\left(a+b+c\right)=a+b+c\)
\(\Rightarrow\left(\frac{a^2}{b+c}+\frac{b^2}{c+a}+\frac{c^2}{a+b}\right)=0\)(đpcm)
a,cho (a/b+c)+(b/c+a)+(c/a+b)=1.cm (a2/b+c)+(b2/c+a)+(c2/a+b)=0
b,cho (x/a)+(y/b)+(z/c)=1va(a/x)+(b/y)+(c/z)=0
cm(x2/a2)+(y2/b2)+(z2/c2)=1
CM: 16^a +16^b +16^c >= 2^a+ 2^b +2^c, biết a+b+c= 0
cho a,b,c>0. CM: a/b + b/a + a/c>= căn a/b + căn b/a+ căn a/c
cho a>b>c>0 và a^2+b^2+c^2=1.cm a^3/(b+c) + b^3/(a+c) +c^3/(a+b)>=1/2
cho 0≤a,b,c≤1, a+b+c=2.CM a^2+b^2+c^2≤2
Cho a, b, c>0 cm
a^2/(b^2+c^2)+b^2/(c^2+a^2)+c^2/(a^2+b^2)>=a/(b+c)+b/(c+a)+c/(a+b)
cho (a+b+c)^2=a^2+b^2+c^2 với a,b,c là 3 số khác 0 .CM 1/a^2 + 1/b^2 + 1/c^2 = 3abc
Cho a/b-c+b/c-a+c/a-b=0
CM: a/(b-c)2+b/(c-a)2+c/(a-b)2=0
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 \(\frac{1}{a+b-c}+\frac{1}{b+c-a}+\frac{1}{c+a-b}\ge\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
CM: 16^a +cho a,b,c>0.1 6^b +16^c >= 2^a+ 2^b +2^c, biết a+b+c= 0
CM: a/b + b/a + a/c>= căn a/b + căn b/a+ căn a/c
