resolva as equações a)x2 -9x+9 = 0 b) 2x2 + 9=x2 -6x c)6x2+x-1=0 d)-16x+8-1=0 e) -9x2+6x-5=0 f)x2+3x-4=0
a) x² - 9x + 9 = 0 a = 1; b = - 9; c = 9 Δ = b² - 4ac Δ = (-9)² -4.1.9 Δ = 81 - 36 Δ = 45 √Δ = √9.√5 √Δ = 3√5 x = - b +/- √Δ = - ( - 9) +/- √45 2a 2.1 x = 9 + 3√5 2 x = 9 - 3√5 2 ***************************** b) 2x² + 9 = x² - 6x 2x² - x² + 6x + 9 = 0 x² + 6x + 9 = 0 a = 1; b = 6; c = 9 Δ = b² -4ac Δ = 6² -4.1.9 Δ = 36 - 36 Δ = 0 x = - b +/- √Δ = - 6 +/- 0 2a 2.1 x = - 6 2 x = - 3 ************************************* c) 6x² + x - 1 = 0 a = 6; b = 1; c = - 1 Δ = b² -4ac Δ = 1² - 4.6.(-1) Δ = 1 + 24 Δ = 25 x = - b +/- √Δ = - 1 +/- √25 2a 2.6 x = - 1 + 5 = 4 (:4) = 1 12 12 (:4) 3 x = - 1 - 5 = - 6 (:6) = - 1 12 12 (:6) 2 _____________________________________ d) - 16x² + 8x - 1 = 0 a = - 16; b = 8; c = - 1 Δ = b² - 4ac Δ = 8² -4.(-16).(-1) Δ = 64 + 64.(-1) Δ = 64 - 64 Δ = 0 x = - b +/- √Δ = - 8 +/- 0 2a 2.(-16) x = - 8 = 8 (:8) = 1 - 32 32 (:8) 4 *********************************************************** e) - 9x² + 6x - 5 = 0 a = - 9; b = 6; c = - 5 Δ = b² - 4ac Δ = 6² - 4.(-9).(-5) Δ = 36 + 36.(-5) Δ = 36 -180 Δ = - 144 (não há solução para os Números Reais) ******************************************************** f) x² + 3x - 4 = 0 a = 1; b = 3; c = - 4 Δ = b² -4ac Δ = 3² -4.1.(-4) Δ = 9 + 16 Δ = 25 x = - b +/- √Δ = - 3 +/- √25 2a 2.1 x = - 3 + 5 = 2/2 = 1 2 x = - 3 - 5 = - 8/2 = - 4 2