SOLUTION: Solve {{{sqrt(2x+1)-sqrt(x)=1}}}

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Question 143039: Solve sqrt%282x%2B1%29-sqrt%28x%29=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B1%29-sqrt%28x%29=1 Start with the given equation


sqrt%282x%2B1%29=1%2Bsqrt%28x%29 Add sqrt%28x%29 to both sides


2x%2B1=%281%2Bsqrt%28x%29%29%5E2 Square both sides


2x%2B1=1%2B2sqrt%28x%29%2Bx Foil the right side


2x%2B1-1-x=2sqrt%28x%29 Subtract x from both sides. Subtract 1 from both sides


x=2sqrt%28x%29 Combine like terms


x%5E2=4x Square both sides


x%5E2-4x=0 Subtract 4x from both sides


x%28x-4%29=0 Factor the left side



Now set each factor equal to zero:
x=0 or x-4=0

x=0 or x=4 Now solve for x in each case


So our possible answers are

x=0 or x=4


However, we need to check our answers first


Check:
Let's check the solution x=0


sqrt%282x%2B1%29-sqrt%28x%29=1 Start with the given equation


sqrt%282%280%29%2B1%29-sqrt%280%29=1 Plug in x=0


sqrt%280%2B1%29-sqrt%280%29=1 Multiply


sqrt%281%29-sqrt%280%29=1 Add


1-0=1 Simplify the square roots


1=1 Subtract. So this verifies the solution x=0


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Now let's check the solution x=4

sqrt%282x%2B1%29-sqrt%28x%29=1 Start with the given equation


sqrt%282%284%29%2B1%29-sqrt%284%29=1 Plug in x=4


sqrt%288%2B1%29-sqrt%284%29=1 Multiply


sqrt%289%29-sqrt%284%29=1 Add


3-2=1 Simplify the square roots


1=1 Subtract. So this verifies the solution x=4




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Answer:

So the solutions are

x=0 or x=4