Question

Help!
Find the non-extraneous solutions of
sqrtx+6 - 5 = x + 1

A. x = −2

B. x = −6

C. x = −6 and x = −2

D. x = 2


I am stuck with (x+6)^1/2 = x +6

Answer 1

as you have
(x+6)^1/2 = x +6

squaring both sides we get

x+6 = (x+6)^2

can you do it from here

Answer 2

#1 thing to do is to WRITE DOWN \(x + 6 \ge 0 \implies x \ge -6\)

#2 thing to do is add 5, as you have done.

#3 thing to do is think about it and stop manipulating symbols for a moment. What two numbers are their own square roots?

#4 thing to do Solve
x + 6 = One of them
x + 6 = The other one

#5 thing to do, after identifying the two possible solutions, and solving, compare them to -6.