Question

2. Resolva as seguintes equações de segundo grau
a) x²-5x+6=0
b) x²-8x+12=0
c) x² + 2x - 8 = 0
d) 2x²-8x+8 = 0​

Answer 1

Explicação passo-a-passo:

$formulas: \\∆ = {b}^{2} - 4.a.c \\ x _{1} = \frac{ - b + \sqrt{∆} }{2.a} \\ x _{2} = \frac{ - b - \sqrt{∆} }{2.a} \\ \\ \\ \\ {x}^{2} - 5x + 6 = 0 \\∆ = {5}^{2} -4.6. \\ ∆ =25 - 24 = 1 \\ x _{1} = \frac{5 + 1}{2} = \frac{6}{2} = 3 \\ x _{2} = \frac{5 - 1}{2} = \frac{4}{2} = 2\\ \\ \\ {x}^{2} - 8x + 12 = 0 \\ ∆ = {8}^{2} - 4.12 \\ ∆ = 64 - 48 = 16 \\ \sqrt{∆} = 4 \\ x _{1} = \frac{8 + 4}{2} = \frac{12}{2} = 6 \\ x _{2} = \frac{8 - 4}{2} = \frac{4}{2} = 2\\ \\ {x}^{2} + 2x - 8 = 0 \\ ∆ = {2}^{2} - 4.1. - 8 \\ ∆ = 4 + 32 = 36 \\ \sqrt{∆} = 6 \\ x _{1} = \frac{ - 2 + 6}{2} = \frac{4}{2} = 2 \\ x _{2} = \frac{ - 2 - 6}{2} = \frac{ - 8}{2} = - 4 \\ \\ 2 {x}^{2} - 8x + 8 = 0 \\ ∆ = 64 - 4.8.2 \\ ∆ = 64 - 64 = 0 \\ x = \frac{8 + 0}{4} = 2$