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números M y N.
1) M-N = 6
2) M²+N² = 116
de modo que despejando de 1 :
M= N+6
Sustituyendo en 2:
(N+6)²+N = 116
N²+12N + 36 +N² = 116
2N²+12N-80=0
N= 4
Entonces M = N+6 = 4+6 = 10
Los números son 10 y 4