Odpowiedź:
w(x) = ax⁴ - 3x³ + bx² - 8
w(-1) = 7 1/3
w(3) = 46
w(- 1) = a * (- 1)⁴ - 3 * ( - 1)³ + b * ( - 1)² - 8 = a + 3 + b - 8 = a + b - 5
w(3) = a * 3⁴ - 3 * 3³ + b * 3² - 8 = 81a - 81 + 9b - 8 = 81a + 9b - 99
a + b - 5 = 7 1/3
81a + 9b - 99 = 46
a + b = 7 1/3 + 5 = 12 1/3 | * 9
81a + 9b = 46 + 99 = 145
9a + 9b = 12 1/3 * 9
81a + 9b = 145
9a + 9b =37/3 * 9
81a + 9b = 145
9a + 9b = 37 * 3
81a + 9b = 145
9a + 9b = 111
81a+ 9b = 145
Odejmujemy równania
9a - 81a + 9b - 9b = 111 - 145
- 72a = - 34
72a = 34
a =34/72 = 17/36
a + b = 7 1/3
17/36 + b = 7 1/3
b = 7 1/3 - 17/36 = 7 12/36 - 17/36 = 6 48/36 - 17/36 = 6 31/36
Odp: a = 17/36 , b = 6 31/36
