Question

Jika a(lfa) dan b(eta) akar-akarnya 2x²-14x+3k-4=0 dan a(lfa)² - b(eta)²=21. Tentukan nilai k.

Answer 1

2x² - 14x + 3k - 4
α + β = - ( -14/2)
α + β =  7
α =  7 - β

α² - β² = 21
(α - β)(α + β) = 21
(7 - β - β)( 7 ) = 21
(7 - 2β) = 21 : 7
7 - 2β =  3
- 2β = - 3 - 7
- 2β = - 10
β = 5

α = 7 - β
α = 7 - (5)
α = 2


αβ = (3k - 4) / 2
(5)(2) = (3k - 4)/2
10 = (3k - 4)/2
20 = 3k - 4
20 + 4 = 3k
24 = 3k
k = 8