a/a' + b'/b = 1 <=> ab + a'b' = a'b <=> abc + a'b'c = a'bc (1) (vì c # 0)
b/b' + c'/c = 1 <=> bc + b'c' = b'c <=> a'bc + a'b'c' = a'b'c (2) (vì a' # 0)
(1) + (2) => đpcm
Biết\(\frac{a}{a'}+\frac{b'}{b}=1\);\(\frac{b}{b'}+\frac{c'}{c}=1\)CMR abc+a'b'c'=1
cho abc khác 0 tm:a+b+c khác 0 và\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}\)
CMR:\(\frac{1}{a^{2005}}+\frac{1}{b^{2005}}+\frac{1}{c^{2005}}=\frac{1}{a^{2005}+b^{2005}+c^{2005}}\)
cho a3+b+c=3abc và abc#0 và a+b+c#0
cmr P=(\(\frac{1}{a}+\frac{1}{b}\))\(\left(\frac{1}{b}+\frac{1}{c}\right)\left(\frac{1}{c}+\frac{1}{a}\right)\)=\(\frac{8}{abc}\)
cho a,b,c>0 CMR
\(\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\left(\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\right)\ge\frac{9}{1+abc}\)
Cho a,b,c>0
Cmr
\(\frac{1}{a^3+b^3+abc}+\frac{1}{b^3+c^3+abc}+\frac{1}{a^3+c^3+abc}\le\frac{1}{abc}\)
Cho a,b,c >0. CMR:
\(\frac{1}{a^3+b^3+abc}+\frac{1}{b^3+c^3+abc}+\frac{1}{c^3+a^3+abc}\le\frac{1}{abc}\)
Cho a+ b+ c = abc va a , b ,c >0 . CMR : a + b + c >=\(3\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
Cho a,b,c>0:
\(CMR:\frac{1}{a(b+1)}+\frac{1}{b(c+1)}+\frac{1}{c(a+1)}\geq \frac{3}{abc+1}\)
CMR: Nếu\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\)và a+b+c=abc thì ta có \(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=2\)
