1) Determine os valores de K, m e n para que : 5x²-19x+18=k.(x-2).(x-3)+m.(x-1).(x-3)+n.(x-1).(x-2)
Ola Joao Paulo
5x² - 19x + 18 = k*(x-2)*(x-3) + m*(x-1)*(x-3) + n*(x-1)*(x+2)
k*(x² - 5x + 6) + m*(x² - 4x + 3) + n*(x² + x - 2)
k + m + n = 5
-5k - 4m + n = -19
6k + 3m - 2n = 18
-2k - 2m - 2n = -10
10k + 8m - 2n = 38
2n = -2k - 2m + 10
2n = 10k + 8m - 38
2n = 6k + 3m - 18
-2k - 2m + 10 = 10k + 8m - 38
10k + 8m - 38 = 6k + 3m - 18
12k + 10m = 48
4k + 5m = 20
8k + 10m = 40
4k = 8
k = 2
8 + 5m = 20
5m = 12
m = 12/5
2n = 12 + 36/5 - 18
2n = 36/5 - 30/5 = 6/5
n = 3/5
pronto
Copyright © 2024 1QUIZZ.COM - All rights reserved.
Answers & Comments
Verified answer
Ola Joao Paulo
5x² - 19x + 18 = k*(x-2)*(x-3) + m*(x-1)*(x-3) + n*(x-1)*(x+2)
k*(x² - 5x + 6) + m*(x² - 4x + 3) + n*(x² + x - 2)
k + m + n = 5
-5k - 4m + n = -19
6k + 3m - 2n = 18
-2k - 2m - 2n = -10
10k + 8m - 2n = 38
6k + 3m - 2n = 18
2n = -2k - 2m + 10
2n = 10k + 8m - 38
2n = 6k + 3m - 18
-2k - 2m + 10 = 10k + 8m - 38
10k + 8m - 38 = 6k + 3m - 18
12k + 10m = 48
4k + 5m = 20
8k + 10m = 40
4k = 8
k = 2
8 + 5m = 20
5m = 12
m = 12/5
2n = 6k + 3m - 18
2n = 12 + 36/5 - 18
2n = 36/5 - 30/5 = 6/5
n = 3/5
pronto