Question

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

Answer 1

For this case we must solve the following equation:

$\sqrt {4x ^ 2} - \sqrt {x ^ 2} = 6$

To solve we follow the steps below:

We square both sides of the equation squared:

$(\sqrt {4x ^ 2} - \sqrt {x ^ 2}) ^ 2 = 6 ^ 2\\(\sqrt {4x ^ 2}) ^ 2-2 (\sqrt {4x ^ 2}) (\sqrt {x ^ 2}) + (\sqrt {x ^ 2}) ^ 2 = 36\\4x ^ 2-2 (\sqrt {4x ^ 2 * x ^ 2}) + x ^ 2 = 36\\4x ^ 2-2 (\sqrt {4x ^ 4}) + x ^ 2 = 36\\4x ^ 2-2 (2x ^ 2) + x ^ 2 = 36\\4x ^ 2-4x ^ 2 + x ^ 2 = 36\\x ^ 2 = 36\\x = \pm \sqrt {36}\\x = \pm6$

We choose the positive value because we talk about $. $x = 6$

Answer:

$6