Question

Rút gọn các biểu thức sau:

a) \(x\) + 3 + \(\sqrt{x^2-6x+9}\) ( \(x\)≤3 )

b) \(\sqrt{x^2+4x+4}-\sqrt{x^2}\) ( -2≤\(x\)≤0 )

Answer 1

a) \(=x+3+\sqrt{\left(x-3\right)^2}=x+3+3-x=3+3=6\)
b) \(=\sqrt{\left(x+2\right)^2}-\sqrt{x^2}=x+2+x=2x+2\)

Answer 2

a) 

\(x+3+\sqrt{x^2-6x+9}\)

\(=x+3+\sqrt{x^2-2.3.x+3^2}\)

\(=x+3+\sqrt{\left(x-3\right)^2}\)

\(=x+3+\left|x-3\right|\)

\(=x+3+3-x\) (vì \(x\le3\) nên \(x-3\le0\))

\(=6\)

b)

\(\sqrt{x^2+4x+4}-\sqrt{x^2}\)

\(=\sqrt{x^2+2.2.x+2^2}-\left|x\right|\)

\(=\sqrt{\left(x+2\right)^2}+x\) (vì \(x\le0\))

\(=\left|x+2\right|+x\)

\(=x+x+2\) (vì \(x\ge-2\) nên \(x+2\ge0\))

\(=2x+2\)

Answer 3

a, \(x+3+\sqrt{\left(x-3\right)^2}=x+3+\left|3-x\right|=x+3+3-x=6\)

b, \(\sqrt{\left(x+2\right)^2}-\sqrt{x^2}=\left|x+2\right|-\left|x\right|=x+2+x=2x+2\)