Question

Consider the radical equation √c+22 = c + 2.

Which statement is true about the solutions c = 3 and c = –6?
Can someone please help me with this, and the last one I worked on

Answer 1

First square both sides to get:

c + 22 = (c + 2)^2

or

c + 22 = c^2 + 4c + 4

Move the terms on the left side to the right side:

c^2 + 3c - 18 = 0

Factor to get:

(c + 6) * (c - 3) = 0.

The solutions are c = -6 and c = 3.

Check to see if these answers work by plugging them into the original equation:

c = -6:

sqrt (-6 + 22) ?= -6 + 2

But, -6 + 2 is a negative number, and you can't get a negative from a square root. So, -6 is extraneous.

c = 3:

sqrt (3 + 22) ?= 3 + 2

5 = 5. So, 3 works.

The answer is: B