Question

Найдите m и n (подбором) 401*5=(m-n)(m+n)

Answer 1

Решение смотри на фото

Answer 2

Решения в целых числах составляются восемью системами уравнений:

m – n = 401 и m + n = 5.
m = 203 и n = –198.

m – n = –401 и m + n = –5.
m = –203 и n = 198.

m – n = 5 и m + n = 401.
m = 203 и n = 198.

m – n = –5 и m + n = –401.
m = –203 и n = –198.

m – n = 2005 и m + n = 1.
m = 1003 и n = –1002.

m – n = –2005 и m + n = –1.
m = –1003 и n = 1002.

m – n = 1 и m + n = 2005.
m = 1003 и n = 1002.

m – n = –1 и m + n = –2005.
m = –1003 и n = –1002.

ответ: (m, n) = (±1003, ±1002) = (±203, ±198).