SOLUTION: (7) Question: How many solutions for x are there in this equation: sqrt x-4 - sqrt x+8 =2? DO NOT count extraneous solutions. (A) 0 (B) 1 (C) 2 (D) 3 Please be specific a

Algebra ->  College  -> Linear Algebra -> SOLUTION: (7) Question: How many solutions for x are there in this equation: sqrt x-4 - sqrt x+8 =2? DO NOT count extraneous solutions. (A) 0 (B) 1 (C) 2 (D) 3 Please be specific a      Log On


   

Question 30455: (7) Question:
How many solutions for x are there in this equation:
sqrt x-4 - sqrt x+8 =2?
DO NOT count extraneous solutions.
(A) 0
(B) 1
(C) 2
(D) 3
Please be specific as to which letter answer is correct. Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I get 1 solution
(B) is the answer
sqrt%28x-4%29+-+sqrt%28x%2B8%29+=+2
sqrt%28x+-+4%29+=+2+%2B+sqrt%28x+%2B+8%29
square both sides
x+-+4+=+4+%2B+4%2A+sqrt%28x+%2B+8%29+%2B+x+%2B+8
cancel x's, combine terms
4%2Asqrt%28x+%2B+8%29+=+-16
sqrt%28x+%2B+8%29+=+-4
square both sides
x+%2B+8+=+16
x+=+8
check
sqrt(8-4) - sqrt(8+8) = 2
0+%2B-+sqrt%284%29+-+0+%2B-+sqrt%2816%29
+2 -4 = -2
+2 +4 = 6
-2 -4 = -6
-2 +4 = 2
0+-sqrt%284%29+-0+-sqrt%2816%29
is the correct answer (B)