Question 274969
sqrt(4z+1)=3+sqrt(4z-2)

4z+1=(3+sqrt(4z-2))^2

4z+1=9+6*sqrt(4z-2)+4z-2

-6=6*sqrt(4z-2)

-1=sqrt(4z-2)

1=4z-2

4z=3

z=3/4


Check:

sqrt(4z+1)=sqrt(4(3/4)+1)=sqrt(3+1)=sqrt(4)=2

3+sqrt(4z-2)=3+sqrt(4(3/4)-2)=3+sqrt(3-2)=3+sqrt(1)=4


---> Contradiction



Answer: No Solutions