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How do you solve $\sqrt{5 x} = - 5$ $sqrt(5x) = -5$ and find any extraneous solutions?

1 Answer

Jan 25, 2017

This equation has no solutions.

Explanation:

If $t \geq 0$ $t >= 0$ then $\sqrt{t} \geq 0$ $sqrt(t) >= 0$
If $t < 0$ $t < 0$ then $\sqrt{t} = i \sqrt{- t}$ $sqrt(t) = i sqrt(-t)$ is a pure imaginary number with positive imaginary part.

So $\sqrt{5 x} = - 5$ $sqrt(5x) = -5$ has no solutions.

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