Question 56029: I am solving the following equation:
sqrt x-1 = x-3
I get 5 but then I did it again and got 2. HELP! Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! sqrt (x-1) = x-3
square both sides to get:
x-1= x^2-6x+9
x^2-7x+10=0
(x-5)(x-2)=0
x=5 or x=2
Checking these answers:
Checking x=5 you get:
sqrt(5-1)=5-3
2=2
x=5 is a good solution
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Checking s=2 you get:
sqrt(2-1)=2-3
sqrt 1 =-1
1 = -1
That is wrong so x=2 is an extraneous solution which
means it is a solution for the algebra that resulted
while solving the problem but it is not a solution of
the original problem.
Where did it come from? It resulted from squaring the
original problem; that introduced a solution that worked
for the squared expression but not for the original
expression.
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Cheers,
Stan H.
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