\(\frac{2014a}{ab+2014a+2014}+\frac{b}{bc+b+2014}+\frac{c}{ac+c+1}\)
\(=\frac{abc.a}{ab+abca+abc}+\frac{b}{bc+b+abc}+\frac{c}{ac+c+1}\)
\(=\frac{ac}{1+ac+c}+\frac{1}{c+1+ac}+\frac{c}{ac+c+1}=1\left(ĐPCM\right)\)
Giả sử 3 số a b c thỏa mãn abc=2014. C/m
2014a + b + c =1
ab+2014a+2014 bc+b+2014 ac+c+1
Cho 2 so thuc a, b thoa man dieu kien ab= 1, a+ b\(\ne\)0. Tinh gia tri bieu thuc :
P= \(\frac{1}{\left(a+b\right)^3}\left(\frac{1}{a^3}+\frac{1}{b^3}\right)+\frac{3}{\left(a+b\right)^4}\left(\frac{1}{a^2}+\frac{1}{b^2}\right)+\frac{6}{\left(a+b\right)^3}\left(\frac{1}{a}+\frac{1}{b}\right)\)
tim gia tri bieu thuc K=(a+b/a-b +b+c/b-c + c+a/c-a ):(a-b/a+b +b-c/b+c +c-a/c+a) neu cho a,b,c thoa man dieu kien 3(ab+ac+bc) = 2(a^2+b^2+c^2)
cho phan thuc \(\frac{x+1}{x^2+x}\)
a) tim dieu kien cua x de gia tri phan thuc duoc xac dinh
b) rut gon phan thuc
c) tinh gia tri phan thuc tai x = 2014
Tam giac ABC co chu vi bang 1, ba canh a,b,c thoa man dang thuc
\(\frac{a}{1-a}+\frac{b}{1-b}+\frac{c}{1-c}=\frac{3}{2}\)
Chung minh tam giac ABC deu
Cho 3 so thuc a b c \(\ne0\)thoa man \(\left(a+b+c\right)^2=a^2+b^2+c^2\). CMR
\(\frac{a^2}{a^2+2bc}+\frac{b^2}{b^2+2ac}+\frac{c^2}{c^2+2ab}=\frac{bc}{a^2+2bc}+\frac{ac}{b^2+2ac}+\frac{ab}{c^2+2ab}\)
Cho a,b,c la cac so nguyen duong thoa man: abc=1. CMR
\(\frac{1}{a^3\left(b+c\right)}+\frac{1}{b^3\left(c+a\right)}+\frac{1}{c^3\left(a+b\right)}\ge\frac{3}{2}\)
Cho a+b+c=2014 và \(\frac{1}{a+b}+\frac{1}{a+c}+\frac{1}{b+c}=\frac{1}{2014}\).Tính S=\(\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}\)
Cho a,b,c thoa man a+b+c=2018 va \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{2018}\).
Chung minh co it nhat mot so la 2018
