Question

\(a.\sqrt{x^2+6x+9}=x-1\)

\(b.\sqrt{x^2+2x}2\sqrt{2=0}\)

\(c.\sqrt{x-1}=\sqrt{2x+3}\)

Answer 1

c. \(\sqrt{x-1}=\sqrt{2x+3}\)

\(\Leftrightarrow\sqrt{\left(x-1\right)^2}=\sqrt{\left(2x+3\right)^2}\)

\(\Leftrightarrow|x-1|=|2x+3|\)

\(\Leftrightarrow x-1=2x+3\)

\(\Leftrightarrow x-2x=3+1\)

\(\Leftrightarrow-x=4\)

\(\Leftrightarrow x=-4\)

KL:

Answer 2

a: =>|x+3|=x-1

\(\Leftrightarrow\left\{{}\begin{matrix}x>=1\\\left(x+3-x+1\right)\left(x+3+x-1\right)=0\end{matrix}\right.\Leftrightarrow x\in\varnothing\)

c: =>2x+3=x-1

=>x=-4