1. √(x+4)=√(x-1)+1

Question

2. 2√n+3=n

Answer 1

√(x+4)=√(x-1)+1
x+4 = (x-1) + 2√(x-1) + 1
4 = 2√(x-1)
16 = 4(x-1)
x = 5

check: √9 = √4+1

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2√n + 3 = n
2√n = n-3
4n = n^2 - 6n + 9
n^2 - 10n + 9 = 0
(n-1)(n-9) = 0
n = 1 or 9

check:
2√1 + 3 = 1? nope - spurious solution
2√9 + 3 = 9? ok

Answer 2

2- n=t^ ---> √n=t 2t+3=t^ t^-2t-3
D=4-(4*(-3))=16 t1=(-(-2)+√D)\2
t1=2+4\2 3 t2=(-(-2)-√D)\2 t2=-1
n=3 n=1 is not correct that √-1 is not true