Question

Cho a > 2 , b >2 . Chứng minh ab >a+b

Answer 1

Vì a >2\(\Rightarrow\)a=2+m,b>2\(\Rightarrow\)b=2+n (m,n\(\in\)N*)

\(\Rightarrow\)a.b=(2+m).(2+n)=2.(2+n)+m.(2+n)= 4+2n+2m+mn=4+m+n+m+n+mn=(4+m+n)+(m+n+mn)=2m+2n+(m+n+mn)>(2+m)+(2+m)=a.b(đpcm)

Answer 2

Theo đề bài ta có:

\(\left\{{}\begin{matrix}a>2\Rightarrow a=2+m\\b>2\Rightarrow b=2+n\end{matrix}\right.\) với \(m;n\in N\)

\(\Rightarrow\left\{{}\begin{matrix}ab=\left(2+m\right)\left(2+n\right)\\a+b=4+m+n\end{matrix}\right.\)

\(\Rightarrow ab=4+2n+2m+mn\)

Dễ thấy: \(4+2n+2m>4+m+n\)

\(\Rightarrow ab>a+b\)

\(\rightarrowđpcm\)