\(\sqrt{x^2-4x+4}\) vs x>2

b,3x+

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9 tháng 7 2019

a) \(4x-\sqrt{x^2-4x+4}=4x-\sqrt{\left(x-2\right)^2}=4x-\left(x-2\right)=3x+2\)

b) \(3x+\sqrt{9+6x+x^2}=3x+\sqrt{\left(x+3\right)^2}=3x-\left(x+3\right)=2x-3\)

c) \(\frac{x+6\sqrt{x}+9}{x-9}=\frac{\left(\sqrt{x}+3\right)^2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\frac{\sqrt{x}+3}{\sqrt{x}-3}\)

d) \(\frac{\sqrt{x^2+4x+4}}{x+2}=\frac{\sqrt{\left(x+2\right)^2}}{x+2}=\frac{\left|x+2\right|}{x+2}\)( 1 )

với x < -2 thì : \(\left(1\right)\Leftrightarrow\frac{-\left(x+2\right)}{x+2}=-1\)

với x > -2 thì : \(\left(1\right)\Leftrightarrow\frac{\left(x+2\right)}{x+2}=1\)

7 tháng 7 2017

a,=\(4x-\sqrt{\left(x-2\right)^2}\)

=\(4x-x+2\)

=3x+2

b,\(3x+\sqrt{\left(x+3\right)^2}\)

=\(3x+x+3\)

=4x+3

8 tháng 6 2019

a/ \(=4x-\sqrt{\left(x-2\right)^2}=4x-x+2=3x+2\)

b/ \(=3x+\sqrt{\left(x+3\right)^2}=3x+x+3=4x+3\)

c/ xem lại đb

d/ \(=\frac{\sqrt{\left(x+2\right)^2}}{x+2}=\frac{x+2}{x+2}=1\)

26 tháng 8 2020

a) \(x+3+\sqrt{x^2-6x+9}\left(x\le3\right)\)

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

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

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

\(=x+3-x+3\)

\(=6\)

b) \(\sqrt{x^2+4x+4}-\sqrt{x^2}\left(-2\le x\le0\right)\)

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

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

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

\(=x+2+x\)

\(=2x+2=2\left(x+1\right)\)

c) \(\frac{\sqrt{x^2-2x+1}}{x-1}\left(x>1\right)\)

\(=\frac{\sqrt{\left(x-1\right)^2}}{x-1}\)

\(=\frac{\left|x-1\right|}{x-1}\)

\(=\frac{x-1}{x-1}=1\)

d) \(\left|x-2\right|+\frac{\sqrt{x^2-4x+4}}{x-2}\)

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

\(=\left|x-2\right|+\frac{\left|x-2\right|}{x-2}\)

\(=\left|x-2\right|+\frac{-\left(x-2\right)}{x-2}\)

\(=\left|x-2\right|-1\)

\(=-\left(x-2\right)-1\)

\(=-x+2-1\)

\(=-x+1=-\left(x-1\right)\)

28 tháng 7 2016

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

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

\(=x+3+x-3\)

\(=2x\)

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

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

\(=x+2-x\)

=2

c)\(\sqrt{\frac{x^2-2x+1}{x-1}}\)

\(=\sqrt{\frac{\left(x-1\right)^2}{x-1}}\)

\(=\sqrt{x-1}\)