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

Answer by HyperBrain(694) About Me  (Show Source):
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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