jika log (2x²-9x+22=1 mempunyai akar p dan q tentukan nilai 2p³+2q³

jawab

2x² - 9x + 22 = 10
2x² - 9x + 12 = 0
 p+ q = 9/2
p q = 6

2(p³+q³) = 2 {(p+q)³ - 3pq (p+q)}
= 2 {(9/2)³ - 3(6)(9/2)}
= 2 ( 729/8 - 81)
 =2 (81/8)
= 81/4

LogAritMa

log (2x² - 9x + 22) = 1
log (2x² - 9x + 22) = log 10
2x² - 9x + 22 = 10
2x² - 9x + 12 = 0
p + q = -b/a = 9/2
pq = c/a = 12/2 = 6

••
2p³ + 2q³
= 2(p³ + q³)
= 2(p + q)((p + q)² - 3pq)
= 2 (9/2)((9/2)² - 18)
= 9(81/4 - 72/4)
= 9 × 9/4
= 81/4
= 20 1/4 ✔