Question

Determinati n aparttine Z pentru care urmatoarele numere reprezinta un patrat perfect:
a) n²+ 9
b) n²+2n+13
c) n²-4n+20

Answer 1

a) n²+ 9;          4²+9=25=5²  ;  n=4
b) n²+2n+13;  1²+2×1+13=16=4²;  n=1
c) n²-4n+20;   2²−4×2+20=16=4²; n=2

Answer 2

n^2+9=25=>n^2=25-9=16, n=4 n^2+2n+13=16=>n^2+2n=3, n=1 n^2-4n+20=16=>n^2-4n=4, n=2