Question

So sánh:

\(\sqrt{2003}+\sqrt{2004}\) và \(2\sqrt{2004}\)

Answer 1

\(\sqrt{2003}\)\(+\)\(\sqrt{2004}\)\(>\)\(2\)\(\sqrt{2004}\)

k mik nha

Answer 2

Đặt \(A^2=\left(\sqrt{2003}+\sqrt{2004}\right)^2>0\)

\(\le\left(1+1\right)\left(2003+2004\right)=2\cdot4007=8014\)

\(\Rightarrow A^2\le8014\). Và 

\(B^2=\left(2\sqrt{2004}\right)^2=4\cdot2004=8016\)

Suy ra \(A^2\le8014< 8016=B^2\Leftrightarrow A< B\)