f(x) = x^2 + px + q
f(1) = 1 + p*1 + q = 1 + p + q; f(-1) = 1 + p(-1) + q = 1 - p + q
f(2) = 4 + 2p + q; f(-2) = 4 - 2p + q
Первое равенство:
f(1)*f(-1) = f(2)*f(-2)
(1 + p + q)(1 - p + q) = (4 + 2p + q)(4 - 2p + q)
1+p+q-p-p^2-pq+q+pq+q^2 = 16+8p+4q-8p-4p^2-2pq+4q+2pq+q^2
1 + 2q + q^2 - p^2 = 16 + 8q - 4p^2 + q^2
4p^2 - p^2 = 8q - 2q + 16 - 1
3p^2 = 6q + 15
p^2 = 2q + 5
q = (p^2 - 5)/2
Второе равенство:
f(3) = 9 + 3p + q = 2
(p^2 - 5)/2 + 3p + 7 = 0
p^2 - 5 + 6p + 14 = 0
p^2 + 6p + 9 = 0
(p + 3)^2 = 0
p = -3; q = (p^2 - 5)/2 = (9 - 5)/2 = 4/2 = 2
Приведенный квадратный трехчлен:
f(x) = x^2 - 3x + 2
f(-3) = 9 - 3*(-3) + 2 = 9 + 9 + 2 = 20
