How do you solve $sqrt(x+3) + 5 = 0$ and find any extraneous solutions?

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Answer 1 · 2017-03-05T23:33:15

This equation has no solutions.

Note that for any Real value of $x$ one of the following holds:

$x + 3 >= 0" "$ and $" "sqrt(x+3) >= 0$
$x + 3 < 0" "$ and $" "sqrt(x+3) = (sqrt(-x-3))i" "$ is pure imaginary with positive imaginary part.

In particular $sqrt(x+3)$ cannot be a negative Real number if $x$ is Real.

Hence the given equation has no Real solution.

How do you solve sqrt(x+3) + 5 = 0sqrt(x+3) + 5 = 0 and find any extraneous solutions?