Thay abc = 1 ta có:
\(\dfrac{1}{ab+a+1}+\dfrac{b}{bc+b+1}+\dfrac{1}{abc+bc+b}\)
\(=\dfrac{abc}{ab+a+abc}+\dfrac{b}{bc+b+1}+\dfrac{1}{1+bc+b}\)
\(=\dfrac{abc}{a\left(b+1+bc\right)}+\dfrac{b}{bc+b+1}+\dfrac{1}{bc+b+1}\)
\(=\dfrac{bc}{bc+b+1}+\dfrac{b}{bc+b+1}+\dfrac{1}{bc+b+1}\)
\(=\dfrac{bc+b+1}{bc+b+1}=1\)
Vậy \(\dfrac{1}{ab+a+1}+\dfrac{b}{bc+b+1}+\dfrac{1}{abc+bc+1}=1\)
Cho tan giác ABC có: \(\widehat{C}=2\widehat{B}=4\widehat{A}\). CMR: \(\dfrac{1}{AB}+\dfrac{1}{AC}=\dfrac{1}{BC}\)
Cho tam giác ABC có \(\widehat{C}=2\widehat{B}=4\widehat{A}\). CMR: \(\dfrac{1}{AB}+\dfrac{1}{AC}=\dfrac{1}{BC}\)
Cho ab,c thuộc R, CM:
\(\dfrac{a}{bc}+\dfrac{b}{ca}+\dfrac{c}{ab}\ge\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\left(vớia,b,c>0\right)\)
Cho a.b.c= 1. Tính \(\dfrac{a}{ab+a+1}+\dfrac{b}{bc+b+1}+\dfrac{c}{ac+c+1}\)
Cho a,b,c >0 và a2 + b2 + c2 = 1 . CMR
\(\dfrac{1}{1-ab}+\dfrac{1}{1-bc}+\dfrac{1}{1-ca}\le\dfrac{9}{2}\)
Cho \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=0\). Tính giá trị biểu thức:
P\(=\dfrac{ab}{c^2}+\dfrac{bc}{a^2}+\dfrac{ca}{b^2}\)
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 3 số thưc dương thỏa mãn abc=1 . Cmr . \(\dfrac{a}{a^{3\:}+a+1\:\:\:}+\dfrac{b}{b^3+b+1}+\dfrac{C}{c^3+C+1\:}\le1\)
Cho abc khác 0, \(a^3+b^3+c^3=3abc\) . Tính A= \(\left(1+\dfrac{a}{b}\right).\left(1+\dfrac{b}{c}\right).\left(1+\dfrac{c}{a}\right)\)
