SOLUTION: For the following, solve. Find exact solutions {{{x-2*sqrt(x)+1=0}}}

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Question 142978: For the following, solve. Find exact solutions

x-2%2Asqrt%28x%29%2B1=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x-2%2Asqrt%28x%29%2B1=0 Start with the given equation

Let y=sqrt%28x%29. So this means that y%5E2=%28sqrt%28x%29%29%5E2=x


y%5E2-2y%2B1=0 Replace sqrt%28x%29 with y replace x with y%5E2



%28y-1%29%28y-1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
y-1=0 or y-1=0

y=1 or y=1 Now solve for y in each case


Since we have a repeating answer, our only answer is y=1


Remember, we let y=sqrt%28x%29

So this means that sqrt%28x%29=1

x=1%5E2 Square both sides

x=1 Simplify


So our answer is x=1