SOLUTION: solve. sqrt x-1=x-3

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Question 120471: solve. sqrt x-1=x-3
Answer by nabla(475) About Me  (Show Source):
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sqrt%28x-1%29=x-3
x-1=%28x-3%29%5E2 (Square both sides)
x-1=x%5E2-6x%2B9 (Expand binomial)
0=x%5E2-7x%2B10 (subtract (x-1) from both sides)
0=%28x-5%29%28x-2%29 (factor right side)
giving the following two equations
x-5=0 or x-2=0
which implies x=5 or x=2,
but x=2 gives 1=-1 when substituted into the original equation, thus we exclude this solution, leaving x=5 as the solution to this problem.