Question 214026
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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(3q+1) - sqrt(q-1) = 2}}}
{{{sqrt(3q+1)= 2+sqrt(q-1)}}}
Square both sides
{{{3q+1 = 4+(q-1)+4sqrt(q-1)}}}
{{{3q+1 = q+3+4sqrt(q-1)}}}
{{{2q-2 = 4sqrt(q-1)}}}
{{{q-1 = 2sqrt(q-1)}}}
Let x=q-1
Then
{{{x = 2sqrt(x)}}}
{{{x^2 = 4x}}}   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<<<---===  this is the place where @HyperBrain made his error. &nbsp;&nbsp;&nbsp;&nbsp;I fixed it.
{{{x^2-4x=0}}}
{{{x(x-4)=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=<u>1 or 5</u>


Solved correctly.