Theo đề bài ta có \
\(\hept{\begin{cases}a>b;c>d\\ab=cd\\a>c\end{cases}}\)
\(\Rightarrow c>d>b\)(vì nếu \(d\le b\)thì \(ab>cd\))
Ta cần chứng minh
\(a+b>c+d\)
\(\Leftrightarrow\frac{cd}{b}+b>c+d\)
\(\Leftrightarrow cd+b^2>cb+db\)
\(\Leftrightarrow\left(cd-cb\right)+\left(b^2-db\right)>0\)
\(\Leftrightarrow\left(d-b\right)\left(c-b\right)>0\)(đúng)
\(\Rightarrow\)ĐPCM