Question

Misalkan selisih kuadrat akar-akar persamaan x2 - (2m+ 4)x+8m =0 sama dengan 20. Maka nilai m2 - 4

Answer 1

(x₁ - x₂) = 20
√D/a = 20
(√(b² - 4ac))/a = 20
(√(-(2m + 4)² - 4(1)(8m)) / 1 = 20
√(-(2m + 4)² - 4(1)(8m) = 20
(2m + 4)² - 4(1)(8m) = 400
4m² + 16m + 16 - 32m = 400
4m² - 16m + 16 = 400
4m² - 16m - 384 = 0
m² - 4m - 96 = 0
(m + 8) (m - 12) = 0
m + 8 = 0 \/ m - 12 = 0
m = -8 \/ m = 12

⇒ m = -8
m² - 4
= (-8)² - 4
= 64 - 4
= 60

⇒ m = 12
m² - 4
= (12)² - 4
= 144 - 4
= 140