Question

Answer 1

a)
\(\sqrt{\left(2x+1\right)^2}=3\)
TH1 x \(\ge\) -1/2
2x+1=3
2x=2
x=1
TH2 x< -12
1-2x=3
-2x=2
x=-1
 

Answer 2

Bài 2a) pt

<=> sqrt((2x + 1)^2) = 3

<=> |2x + 1| = 3

<=> 2x + 1 = 3 hoặc 2x + 1 = -3

<=> x = 1 hoặc x = -2

 

Answer 3

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

\(\Leftrightarrow\left|2x+1\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=3\\2x+1=-3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)

b) \(\Leftrightarrow\sqrt{x^2+9}=-2+x\left(đk:x\ge2\right)\)

\(\Leftrightarrow x^2+9=4-4x+x^2\)

\(\Leftrightarrow4x=-5\Leftrightarrow x=-\dfrac{5}{4}\)

Answer 4

a) \(\sqrt{4x^2+4x+1}=3\)

\(4x^2+4x+1=9\)

\(4x^2+4x=8\)

\(4\left(x^2+x\right)=8\)

\(x^2+x=2\)

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

\(\Rightarrow x=1\)