SOLUTION: (sqrt of 5-x)+1=x-2 I get x=4 or x=1 but my book says just x=4. I need to know why this is because they will both make the equation equal zero (or at least I think they do) Thanks!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: (sqrt of 5-x)+1=x-2 I get x=4 or x=1 but my book says just x=4. I need to know why this is because they will both make the equation equal zero (or at least I think they do) Thanks!      Log On


   

Question 644842: (sqrt of 5-x)+1=x-2 I get x=4 or x=1 but my book says just x=4. I need to know why this is because they will both make the equation equal zero (or at least I think they do) Thanks!
Found 2 solutions by ewatrrr, richwmiller:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

(sqrt of 5-x)+1=x-2 

sqrt%285-x%29=highlight%28x-3%29   |Note: x = 1, gives sqrt%284%29=highlight%28-2%29  

I get x=4 or x=1, yes...however, x = 1 is an extraneous solution and tossed out..

ONe needs to test solutions in cases involving square roots

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(x-4)*(x-1)=0
yields
x*2-5x+4=0
Does that equal
sqrt(5-x)+1=x-2
no
x=4
sqrt(5-4)+1=4-2
1+1=2
2=2
x=1 doesn't work
sqrt(5-x)+1=x-2
sqrt(5-1)+1=1-2
sqrt(4)+1=-1
2+1=-1
3=-1

not true