Question 214026
{{{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=2x}}}
{{{x^2-2x=0}}}
{{{x(x-2)=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=<u>1 or 3</u>