If (x-a)^0.5=(x+b)^0.5, which of the following must be true? ?

Question

A. a=0

B. b=0

C. a+b=0

D. a-b=0

E. a^2 + b^2 =0

Answer 1

I have to disagree with the first poster's argument. Taking the square root of both sides would result in

+/-(x-a)^0.25 = +/-(x+b)^0.25

Which takes you farther away from the solution.

The easiest thing to do is square both sides to get

x - a = x + b

Subtract x from both sides to get

-a = b

add a to both sides to get

0 = a + b

So the answer is in fact C.

Answer 2

(x-a)^0∙5 = (x+b)^0∙5

√(x-a) = √(x+b)    (Take the square of both sides).

x - a = x + b

x = x + b + a

x - x = b + a

0 = b + a

Answer C.