zadanie 3 rozwiąż równania ; a) x² - 8x-9=0 b) x²-10x= -21 c) 9x²+12x+4=0 d) -4x²+x=0 e) 9x²-16=0

a) x² - 8x - 9 = 0 Δ = b² - 4ac = (-8)² - 4×1×(-9) = 64 + 36 = 100 √Δ = 10 x1 = -b-√Δ/2a = 8 - 10/2 = -2/2 = -1 x2 = -b+√Δ/2a = 8+10/2 = 18/2 = 9 x∈{-1,9} b) x² - 10x = -21 x² - 10x + 21 = 0 Δ = b² - 4ac = (-10)² - 4×1×21 = 100 - 84 = 16 √Δ = 4 x1 = -b-√Δ/2a Δ= 10-4/2 = 6/2 = 4 x2 = -b+√Δ/2a = 10+4/2 = 14/2 = 7 x∈{4,7} c) 9x² + 12x + 4 = 0 Δ = b² - 4ac = 12² - 4×9×4 = 144 - 144 = 0 x0 = -b/2a = -12/2×9 = -12/18 = -6/3 = -2 d) -4x² + x = 0 Δ = b² - 4ac = 1 - 4×(-4)× 0 = 1 - 0 = 1 √Δ = 1 x1 = -b-√Δ/2a = -1-1/2×(-4) = -2/-8 = 1/4 x2 = -b+√Δ/2a = -1+1/-8 = 0/-8 = 0 x∈{0,1/4) e) 9x² - 16 = 0 Δ = b² - 4ac = 0 - 4×9×(-16) = 0 + 576 = 576 √Δ = 24 x1 = -b-√Δ/2a = 0-24/18 = -24/18 = -4/3 = -1 1/3 x2 = -b+√Δ/2a = 0+24/18 = 24/18 = 4/3 = 1 1/3 x∈{-1 1/3, 1 1/3}