Question

1) Resolva as equações do 2º grau:
a) x. (x + 3) = 10

b) x² - 1 = 2. (x - 1)​

Answer 1

Resposta:

a) S =  {2, -5}

b) S =  {1}

Explicação passo a passo:

a) x.(x + 3) = 10

x² + 3x = 10

x² + 3x - 10 = 0

Fazendo por Bhaskara:

a = 1  | b = 3  | c = -10

$\frac{-3 +/- \sqrt{3^{2} - 4. 1.(-10)} }{2.1} \\\\\frac{-3 +/- \sqrt{9 - 4.(-10)} }{2} \\\\\frac{-3+/- \sqrt{9 + 40} }{2} \\\\\frac{-3 +/- \sqrt{49} }{2} \\\\\frac{-3+/- 7}{2} \\\\x' = \frac{-3 + 7}{2} = \frac{4}{2} = 2\\\\x" = \frac{-3-7}{2}= \frac{-10}{2} = -5$

b) x² - 1 = 2.(x - 1)

x² - 1 = 2x - 2

x² - 2x - 1 + 2 = 0

x² - 2x + 1 = 0

a = 1  | b = -2  | c = 1

$\frac{2 +/- \sqrt{(-2)^{2}- 4.1.1} }{2.1} \\\\\frac{2 +/- \sqrt{4 - 4} }{2} \\\\\frac{2 +/- \sqrt{0} }{2} \\\\\frac{2+/- 0}{2} \\\\x = \frac{2}{2} = 1$

BONS ESTUDOS!!!