n+2=√(9+n²+2n+1) ..

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n+2=√(9+n²+2n+1)..n+2=√(9+n²+2n+1)..n+2=√(9+n²+2n+1)..n+2=√(9+n²+2n+1)（n+2）²

n+2=√(9+n²+2n+1) ..
n+2=√(9+n²+2n+1) ..

n+2=√(9+n²+2n+1) ..
n+2=√(9+n²+2n+1)
（n+2）²=9+n²+2n+1
n²+4n+4=9+n²+2n+1
n²+4n+4-9-n²-2n-1=0
2n-6=0
2n=6
n=3