Các câu hỏi tương tự
Chứng minh rằng với a,b,c > 0 thì \(\left(ab+bc+ca\right)\left(\frac{1}{\left(a+b\right)^2}+\frac{1}{\left(b+c\right)^2}+\frac{1}{\left(c+a\right)^2}\right)\ge\frac{9}{4}\)
Help me!
CMR
\(\frac{1}{2}\left[\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-c\right)\left(b-a\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}\right]=\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\)
Cho a,b,c >0; abc=1.CMR:
\(\left(a-1+\frac{1}{b}\right)\left(b-1+\frac{1}{c}\right)\left(c-1+\frac{1}{a}\right)\le1\)
Cho a,b,c >0 Chứng minh rằng:
\(\left(a^3+b^3+c^3\right)\left(\frac{1}{a^3}+\frac{1}{b^3}+\frac{1}{c^3}\right)\ge\frac{3}{2}.\left(\frac{b+c}{a}+\frac{c+a}{b}+\frac{a+b}{c}\right)\)
Đề đúng không sai.Ai làm được cho 3 Tick 3 nick khác nhau.
Cho 3 số a,b,c đôi một phân biệt. CMR:
\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-c\right)\left(b-a\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}=2\left(\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\right)\\ \)
\(CMR:\frac{1}{4}\left(\frac{1}{a}+\frac{1}{b}\right)\ge\frac{1}{a+b}\)
1, Cho \(\frac{a}{b}=\frac{c}{d}\)( b,c,d khác 0; c+đ khác 0). CMR:
\(\frac{ab}{cd}=\frac{\left(a+b\right)^2}{\left(c+\text{d}\right)^2}\)
Cho \(B=\frac{1}{2}+\left(\frac{1}{2}\right)^2+\left(\frac{1}{3}\right)^2+....+\left(\frac{1}{2}\right)^{98}+\left(\frac{1}{2}\right)^{99}\)
CMR : B < 1
\(cho\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)cmr\frac{a}{b}=\frac{a-c}{c-b}\) (a,b,c khác 0; c khác b)