how do i solve y+(y-1)^1/2 =7?

Question

what are the solutions to y+(y-1)^1/2 =7

Answer 1

√(y-1)=7-y

Square: y-1=49-14y+y^2

y^2-15y+50=0=(y-10)(y-5)

So y=10 and y=5; but we need to check in original equation: y=10: √9=7-10=-3 is only true if the negative square root is permitted. We reject this solution because we specifically need the positive root.

y=5: √4=7-5. True. So the solution is y=5.