a) (x+5) + (x+5)² = 0 x+5+x²+10x +25 = 0 x²+11x+30-=0 Δ = 121 - 4*30 = 121 -120 = 1 √Δ = 1 x₁ = (-11+1)/2 = -5 x₂ = (-11-1)/2 = -6 b) (x-4)² - (x-4)² = 0 x²-8x+16-x²+8x-16=0 0=0 x ∈ R c) 10(x-5)² = 25 10(x²-10x+25) = 25 10x² -100x+250 = 25 |:5 2x² - 20x +50 = 5 2x²-20x+45 =0 Δ = 400 - 4*45*2 = 400 - 360 = 40 √Δ = √40 = 2√10 x₁ = (20+2√10)/4 = (10+√10)/2 x₂ = (20-2√10)/4 = (10-√10)/2 d) (x-5) (x-8) (x-3)² = 0 1. x-5 = 0 x₁ = 5 2. x-8 = 0 x₂ = 8 3. (x-3)² = 0 x₃ = 3 e) 8(x²+3x) = o 8x(x+3) = 0 1. 8x = 0 x₁ = 0 2. x+3 = 0 x₂ = -3
a) (x+5) + (x+5)² = 0 (x+5)(1+x+5)=0 (x+5)(x+6)=0 x=-5 lub x=-6 b) (x-4)² - (x-4)² = 0 (x-4)²=(x-4)² x∈R c)10(x-5)² = 25 (x-5)² = 25/10 = (5/√10)² = 5√10/10 = √10/2 (x-5)² - (√10/2)²=0 (x-5 + √10/2)(x-5 - √10/2)=0 x=5-√10/2 lub x=5+√10/2 d) (x-5) (x-8) (x-3)² = 0 x=5 lub x=8 lub x=3 e) 8(x²+3x) = 0 x(x+3)=0 x=0 lub x=-3
