Скалярное произведение векторов

Question

Математика: Скалярное произведение векторов​

oleg1960 · Accepted Answer

F(1) = 1 + p + q
f(-1) = 1 - p + q
f(2) = 4 + 2p + q
f(-2) = 4 - 2p + q
f(3) = 9 + 3p + q = 20; q = 11 - 3p
f(1)*f(-1) = f(2)*f(-2)
(1 + p + q)(1 - p + q) = (4 + 2p + q)(4 - 2p + q)
Раскрываем скобки
1+p+q-p-p^2-pq+q+pq+q^2 = 16+8p+4q-8p-4p^2-2pq+4q+2pq+q^2
Упрощаем
1 + q - p^2 + q = 16 + 4q - 4p^2 + 4q
3p^2 - 15 - 6q = 0
p^2 - 2q - 5 = 0
p^2 - 2(11 - 3p) - 5 = 0
p^2 + 6p - 27 = 0
D/4 = 9 + 27 = 36 = 6^2
p1 = -3 - 6 = -9; q1 = 11 - 3p = 11 - 3(-9) = 11 + 27 = 38
p2 = -3 + 6 = 3; q2 = 11 - 3p = 11 - 3*3 = 11 - 9 = 2
Трехчлен:
f1(x) = x^2 - 9x + 38; f(-3) = 9 - 9(-3) + 38 = 74
f2(x) = x^2 + 3x + 2; f(-3) = 9 + 3(-3) + 2 = 2

Скалярное произведение векторов​

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