Question

Help please!!!!!!!!!!!!!!!!!!!!

Answer 1

9514 1404 393

Answer:

  (c) The solution -6 is an extraneous solution

Step-by-step explanation:

If you solve the equation graphically, you can avoid extraneous solutions. The true solution is x = -1.

You can tell from the equation that the domain will be restricted to values of x that make the radical non-negative:

  x+4 ≥ 0   ⇒   x ≥ -4

Then x=-6 must be an extraneous solution. It arises when the negative square root is used.

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The conventional solution method has you square both sides and solve the resulting quadratic.

  (x +4)² = x +10

  x² +7x +6 = 0

  (x +6)(x +1) = 0   ⇒   x = -6 or -1

The solution x=-6 is not in the domain, so is extraneous.

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Additional comment

Graphical solution is often easier if the equation is in the form f(x) = 0. That form can be had by subtracting one side of the equation from both sides. In the attached, we subtracted √(x+10) from both sides. (We added the negative branch of the square root function to show where the extraneous root comes from.)