Question

Thu gọn biểu thức:

\(\sqrt{\left(a-b\right)^2}+\sqrt{\left(a+b\right)^2}\)

Answer 1

Ta có: \(\sqrt{\left(a-b\right)^2}+\sqrt{\left(a+b\right)^2}\)

\(=\left|a-b\right|+\left|a+b\right|\)

Answer 2

\(\sqrt{\left(a-b\right)^2}+\sqrt{\left(a+b\right)^2}\)

\(=|a-b|+|a+b|\) ( 1 )

Nếu \(a\ge b\) \(\Rightarrow\) \(|a-b|=a-b\)

( 1 ) \(\Rightarrow\) a - b + a + b = 2a

Nếu \(a\le b\) \(\Rightarrow\) \(|a-b|=b-a\)

( 1 ) \(\Rightarrow\) b - a + a + b = 2b