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Find all values of such that .

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Find all values of  such that .

AWESOMEEE  Aug 11, 2015

#2
+18829
+10

Find all values of  such that .

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

heureka  Aug 12, 2015
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#1
+26406
+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
+18829
+10
$$\small{\text{ \begin{array}{rcl} \sqrt{4x^2}-\sqrt{x^2} &=& 6\\ \sqrt{4}\sqrt{x^2}-\sqrt{x^2} &=& 6\\ 2\sqrt{x^2}-\sqrt{x^2} &=& 6\\ \sqrt{x^2} &=& 6 \qquad | \qquad 1^2\\ x^2 &=& 36 \qquad | \qquad \pm\sqrt{}\\ x_{1,2} &=& \pm\sqrt{36} \\ x_{1,2} &=& \pm6 \\ \mathbf{x_1} & \mathbf{=} & \mathbf{6}\\ \mathbf{x_2} & \mathbf{=} & \mathbf{-6} \end{array} }}$$