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

1 Answer
Mar 5, 2017

Answer:

This equation has no solutions.

Explanation:

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.