Question

sqrt(4y+1)-sqrt(y-2)=3

Answer 1

sqrt(4y+1)-sqrt(y-2)=3
sqrt(4y+1) = 3 + sqrt(y-2)
[sqrt(4y+1)] ^2 = [ 3 + sqrt(y-2)] ^2
4y + 1 = 9 + 6 sqrt(y-2) + y -2
4y - y + 1 + 2 - 9 = 6 sqrt(y-2)
3y + 3 - 9 = 6 sqrt(y-2)
3y - 6 = 6 sqrt(y-2)
y - 2 = 2sqrt(y-2)
[y - 2]^2 = [2sqrt(y-2)]^2
(y-2)^2 = 4 ( y - 2)
y^2 -4y +4 = 4y - 8
y^2 - 8y + 12 = 0
(y -6) (y-2) = 0
y = 6 or y = 2