Ix² - 2x+1I I x-1I ----------- + ---------- - 12< 0 x≠2 Ix²-4x+4 I I x-2I |(x-1)²| I x-1I ________ + _____ - 12 < 0 |(x-2)²| I x-2I |(x-1)²| + I(x-1)(x-2)I - 12|(x-2)²| _______________________________ < 0 |(x-2)²| (x-1)² - 12(x-2)² + I(x-1)(x-2)I < 0 x²-2x+1 - 12(x²-4x+4) + I(x-1)(x-2)I < 0 x²-2x+1-12x²+48x-48 + I(x-1)(x-2)I < 0 |x-1|*|x-2| < 11x²-46x+47 dla x∈(-∞,1) -(x-1)*(-(x-2)) < 11x²-46x+47 (x-1)*(x-2) < 11x²-46x+47 x²-3x+2<11x²-46x+47 10x²-43x+45>0 (2x-5)(5x-9)>0 x∈(-∞,1⅘)U(2½,∞) zatem x∈(-∞,1) dla x∈<1,2) -(x-2)(x-1) < 11x²-46x+47 -x²+3x-2<11x²-46x+47 12x²-49x+49>0 (3x-7)(4x-7)>0 x∈(-∞,1¾)U(2⅓; ∞) zatem x∈<1,1¾) dla x∈<2,∞) (x-1)*(x-2) < 11x²-46x+47 x²-3x+2<11x²-46x+47 10x²-43x+45>0 (2x-5)(5x-9)>0 x∈(-∞,1⅘)U(2½,∞) zatem x∈(2½,∞) odp. x∈(-∞,1¾)U(2½,∞)
