Question

2- Dadas as equações do 2º grau abaixo, calcule, cada conjunto solução:
a) x² - 5x + 4 = 0
b) - 2+3x -3 =0
c) x2 - 6x + 9 = 0​

Answer 1

Resposta:

Explicação passo a passo:

Fórmulas:

Δ=$b^2-4*a*c$

x=((-b)±√Δ)÷2*a

a) x² - 5x + 4 = 0         a=1   b=(-5)   c=4

Δ=$(-5)^2-4*1*4$

Δ=$25-16$

Δ=$9$

$x=\frac{-\left(-5\right)\pm \:\sqrt{9}}{2\cdot \:\:1}\\\\x=\frac{-\left(-5\right)\pm \:\sqrt{9}}{2}\\\\x=\frac{-\left(-5\right)\pm \:3}{2}\\\\x1=\frac{-\left(-5\right)+3}{2}\\\\x1=\frac{5+3}{2}\\\\x1=\frac{8}{2}\\\\x1=4\\\\\\x2=\frac{-\left(-5\right)-3}{2}\\\\x2=\frac{5-3}{2}\\\\x2=\frac{2}{2}\\\\x2=1$    

b) - 2+3x -3 =0    x(5/3)

$-2+3x-3=0\\3x-2-3=0\\3x=2+3\\3x=5\\\frac{3x}{3}=\frac{5}{3}\\x=\frac{5}{3}$

c) x^2-6x+9=0​   a=1  b=(-6)  c=9

Δ=(-6)^2-4*1*9

Δ= 36-36

Δ=0

$\x=\frac{-\left(-6\right)\pm \sqrt{\left0}}{2\cdot \:1}\\\\x=\frac{-\left(-6\right)\pm \sqrt{\left0}}{2}\\\\x=\frac{-\left(-6\right)}{2}\\x=3$