Odpowiedzi

2010-02-19T22:55:57+01:00
W(x) = x⁴ - m x³ + n x² - 8
W(2) = W(-2)
W(3) = 82
Wyznacz m oraz n.
W(2) = 2⁴ - m*2³ + n*2² - 8 = 16 -8 m + 4 n - 8 = 8 - 8 m + 4 n
W(-2) =(-2)⁴ - m*(-2)³ + n *(-2)² - 8 = 16 + 8 m +4 n - 8 =
= 8 + 8 m + 4 n
czyli
8 - 8 m + 4 n = 8 + 8 m + 4 n
16 m = 0
m = 0
W(3) = 3⁴ - m* 3³ + n * 3² - 8 = 81 - 27 m + 9 n - 8 = 73 -27 m +9 n
czyli
73 - 27 m + 9 n = 82
73 - 27*0 + 9 n = 82
9 n = 82 - 73 = 9
n = 1
Odp. m = 0 oraz n = 1.