+0  
 
0
531
2
avatar+1307 

Find all values of $x$ such that $\sqrt{4x^2} - \sqrt{x^2} = 6$.

AWESOMEEE  Aug 11, 2015

Best Answer 

 #2
avatar+20025 
+10

Find all values of $x$ such that $\sqrt{4x^2} - \sqrt{x^2} = 6$.

 

$$\small{\text{$
\begin{array}{rcl}
\sqrt{4x^2}-\sqrt{x^2} &=& 6\\
\sqrt{4}\sqrt{x^2}-\sqrt{x^2} &=& 6\\
2\sqrt{x^2}-\sqrt{x^2} &=& 6\\
\sqrt{x^2} &=& 6 \qquad | \qquad 1^2\\
x^2 &=& 36 \qquad | \qquad \pm\sqrt{}\\
x_{1,2} &=& \pm\sqrt{36} \\
x_{1,2} &=& \pm6 \\
\mathbf{x_1} & \mathbf{=} & \mathbf{6}\\
\mathbf{x_2} & \mathbf{=} & \mathbf{-6}
\end{array}
$}}$$

heureka  Aug 12, 2015
 #1
avatar+27044 
+10

$$\sqrt{4x^2}-\sqrt{x^2}\rightarrow2|x|-|x|\rightarrow|x|$$

 

|x| = 6 when x = 6 and when x = -6

 

(Perhaps I should note that |x| means the absolute value of x)

.

Alan  Aug 11, 2015
 #2
avatar+20025 
+10
Best Answer

Find all values of $x$ such that $\sqrt{4x^2} - \sqrt{x^2} = 6$.

 

$$\small{\text{$
\begin{array}{rcl}
\sqrt{4x^2}-\sqrt{x^2} &=& 6\\
\sqrt{4}\sqrt{x^2}-\sqrt{x^2} &=& 6\\
2\sqrt{x^2}-\sqrt{x^2} &=& 6\\
\sqrt{x^2} &=& 6 \qquad | \qquad 1^2\\
x^2 &=& 36 \qquad | \qquad \pm\sqrt{}\\
x_{1,2} &=& \pm\sqrt{36} \\
x_{1,2} &=& \pm6 \\
\mathbf{x_1} & \mathbf{=} & \mathbf{6}\\
\mathbf{x_2} & \mathbf{=} & \mathbf{-6}
\end{array}
$}}$$

heureka  Aug 12, 2015

6 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.