Question

Please kaka bantu besok ulangan :'(
Diberikan suku banyak p(x) = 3x˄4 + px˄3 + 2x˄2 -7x – q dengan nilai p(-2) = 66 dan p (2) = 54 hitunglah :
A. nilai p˄2 + q˄2
B. Nilai p˄3 + q˄3

Answer 1

P(x) = 3x^4 + px³ + 2x² - 7x - q

p(-2) = 66
66 = 3(-2)^4 + p(-2)³ + 2(-2)² - 7(-2) - q
66 = 3(16) + (-8)p + 2(4) + 14 - q
66 = 48 - 8p + 8 + 14 - q
66 = 56 - 8p + 14 - q
66 = 70 - 8p - q
-8p - q + 70 - 66 = 0
-8p - q + 4 = 0
-8p - q = -4

p(2) = 54
54 = 3(2)^4 + p(2)³ + 2(2)² - 7(2) - q
54 = 3(16) + 8p + 2(4) - 14 - q
54 = 48 + 8p + 8 - 14 - q
54 = 56 + 8p - 14 - q
54 = 42 + 8p - q
8p - q + 42 - 54 = 0
8p - q - 12 = 0
8p - q = 12

-8p - q = -4
 8p - q = 12
___________  -
-16p     = -16
     p     = -16/-16
     p     =  1

8p - q = 12
8(1) - q = 12
8 - q = 12
-q = 12 - 8
-q = 4
 q = -4

A.)
p² + q² = 1² + (-4)² = 1+16 = 17

B.)
p³ + q³ = 1³ + (-4)³ = 1 + 64 = 65

Maaf, kalau salah..
Semoga bermanfaat.. :) !!

Answer 2

P(-2) = 66 --> 3(-2)^4 + p(-2)^3 + 2(-2)^2 - 7(-2) - q = 66
48 - 8p +8 + 14- q = 66
-8p - q = - 4  atau
8p + q =  4...(1)

p(2) = 54 --> 3(16)+ p(8) + 8- 14 - q = 54
8p - q = 12 ..(2)
..
8p + q = 4
8p - q = 12
16p = 16
p = 1 , q = 4-8 = - 4

a) p^2+ q^2 = 1 + 16 = 17
b) p^3 + q^3 =1- 64 = - 63