SOLUTION: solve the equation: square root of 3q+1 - the square root of q-1 =2

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Question 214026This question is from textbook College algebra
: solve the equation: square root of 3q+1 - the square root of q-1 =2 This question is from textbook College algebra

Found 2 solutions by HyperBrain, ikleyn:
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283q%2B1%29+-+sqrt%28q-1%29+=2
sqrt%283q%2B1%29=2%2Bsqrt%28q-1%29
Square both sides
3q%2B1=4%2B%28q-1%29%2B4sqrt%28q-1%29
3q%2B1=q%2B3%2B4sqrt%28q-1%29
2q-2=4sqrt%28q-1%29
q-1=2sqrt%28q-1%29
Let x=q-1
Then
x=2sqrt%28x%29
x%5E2=2x
x%5E2-2x=0
x%28x-2%29=0
x=0 or x=2
If x=0, q-1=0 so q=1
If x=2, q-1=2 so q=3.
So, q=1 or 3

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
This question is from textbook College algebra
solve the equation: square root of 3q+1 - the square root of q-1 =2
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        The solution in the post by @HyperBrain has an error, which leads to wrong answer.
        His answer is q = 1 or q=3, but q=3 does not satisfy the given equation.

        I came to bring a correct solution.


sqrt%283q%2B1%29+-+sqrt%28q-1%29+=+2
sqrt%283q%2B1%29=+2%2Bsqrt%28q-1%29
Square both sides
3q%2B1+=+4%2B%28q-1%29%2B4sqrt%28q-1%29
3q%2B1+=+q%2B3%2B4sqrt%28q-1%29
2q-2+=+4sqrt%28q-1%29
q-1+=+2sqrt%28q-1%29
Let x=q-1
Then
x+=+2sqrt%28x%29
x%5E2+=+4x         <<<---=== this is the place where @HyperBrain made his error.     I fixed it.
x%5E2-4x=0
x%28x-4%29=0
x=0 or x=4
If x=0, q-1=0 so q=1
If x=4, q-1=4 so q=5.
So, q=1 or 5

Solved correctly.