Question

Dla jakich wartości parametru m równania i mają te same zbiory rozwiązań?

Answer 1

(x-3)(x+2)(x-2)=0
x-3=0  v  x=-2  v  x=2
x∈{-2,2,3}

(x-m)(x+2x-3x-6)=0
(x-m)[x(x+2)-3(x+2)]=0
(x-m)(x+2)(x-3)=0
x-m=x-2
m=2

Answer 2

(x - m)(x² - x - 6) = (x - 3)(x² - 4)
(x - m)(x² - x - 6) = (x - 3)(x + 2)(x - 2)
(x - 3)(x + 2)(x - 2) = 0
x = 3   v  x = -2  v  x = 2
x ∈ {-2; 2; 3}

x² - x - 6 = 0
Δ = b² - 4ac = 1 + 24 = 25
√Δ = 5
x₁ = (1-5)/2 = -2
x₂ = (1+5)/2 = 3
x² - x - 6 = (x + 2)(x - 3)

(x - m) (x + 2)(x - 3) = 0
x - m = x - 2
-m = -2
m = 2