Question

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

Answer 1

9514 1404 393

Answer:

  x = -6 or 6

Step-by-step explanation:

The square root is always positive, so the equation simplifies to ...

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

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The graph shows the solutions to f(x) = 0, where f(x) = √(4x²) -√(x²) -6.