Замените символы * такими одночленами, чтобы выполнялось равенство:
а) $m^2 + 40m + * = (* + 20)^2$;
б) $* - 70pq + * = (7p - *)^2$;
в) $* + 42ac + 49c^2 = (* + *)^2$;
г) $25z^2 - * + * = (* - 8t)^2$.
$m^2 + 40m + *_1 = (*_2 + 20)^2$
$*_1 = 20^2$
$*_1 = 400$
и
$*^2_2 = m^2$
$*_2 = m$
Ответ: $m^2 + 40m + 400 = (m + 20)^2$
$*_1 - 70pq + *_2 = (7p - *_3)^2$
$*_1 = (7p)^2$
$*_1 = 49p^2$
и
$2 ⋅ 7p ⋅ *_3 = 70pq$
$14p ⋅ *_3 = 70pq$
$*_3 = 5q$
и
$*_2 = *^2_3$
$*_2 = (5q)^2$
$*_2 = 25q^2$
Ответ: $49p^2 - 70pq + 25q^2 = (7p - 5q)^2$
$*_1 + 42ac + 49c^2 = (*_2 + *_3)^2$
$*^2_3 = 49c^2$
$*^2_3 = (7c)^2$
$*_3 = 7c$
и
$2 ⋅ *_2 ⋅ *_3 = 42ac$
$2 ⋅ *_2 ⋅ 7c = 42ac$
$14c ⋅ *_2 = 42ac$
$*_2 = 3a$
и
$*_1 = *^2_2$
$*_1 = (3a)^2$
$*_1 = 9a^2$
Ответ: $9a^2 + 42ac + 49c^2 = (3a + 7c)^2$
$25z^2 - *_1 + *_2 = (*_3 - 8t)^2$
$*^2_3 = 25z^2$
$*^2_3 = (5z)^2$
$*_3 = 5z$
и
$*_2 = (8t)^2$
$*_2 = 64t^2$
и
$*_1 = 2 ⋅ *_3 ⋅ 8t$
$*_1 = 2 ⋅ 5z ⋅ 8t$
$*_1 = 80tz$
Ответ: $25z^2 - 80tz + 64t^2 = (5z - 8t)^2$
Пожауйста, оцените решение