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

Explanation:

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

`√(4x^2)-√(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.