Question

Persamaan kuadrat x^2 + (m-1) x -5 = 0 mempunyai akar-akar x1 dan x2.jika x1^2 + x2^2 -2x1x2 = 8m, maka nilai m =...........

Answer 1

= x1^2 + x2^2 - 2x1x2
= (x1 + x2)^2 - 4x1x2 = 8m
= (-(m-1) / 1)^2 - 4 . (-5) = 8m
= m^2 - 2m + 1 + 20 = 8m
= m^2 - 10 m + 21 = 0
= (m - 3)(m-7) = 0
m = 3 atau m = 7

Answer 2

X² + (m-1)x - 5 = 0
x₁ + x₂ = -b/a = -(m-1)/1 = -m+1
x₁ . x₂ = c/a = -5/1 = -5

x₁² + x₂² - 2x₁.x₂ = 8m
(x₁ + x₂)² - 2x₁.x₂ - 2x₁.x₂ = 8m
(x₁ + x₂)² - 4x₁.x₂ = 8m
(-m + 1)² - 4(-5)    = 8m
m² - 2m +1 + 20 - 8m = 0
m² - 10m + 21 = 0
(m - 7) (m - 3) = 0
m = 7 atau m = 3

semoga membantu ya :)