Question

55. Determinaţi pătratele perfecte n pentru care fracţia
5n+1
____
66
este subunitară.​

Answer 1

5n+1/66 -> este subunitara => 5n+1<66 =>n<13

n=1 (A)

n=4 (A)

n=9(A)

n=16(F), 16>13

n€{1, 4, 9}

Answer 2

$\it \dfrac{5n+1}{66} < 1 \Rightarrow 5n+1 < 66\Big|_{-1} \Rightarrow 5n < 65\Big|_{:5} \Rightarrow n < 13\ \ \ \ \ (2)\\ \\ \\ n = p\breve atrat\ perfect\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow n\in\{0,\ \ 1,\ \ 4,\ \ 9\}$