Matemática, perguntado por samueljava13, 8 meses atrás

Aplicando a fórmula de Bhaskara, resolva as seguintes equações do 2º grau:
a) 2x2 - 7x = 15
b) x2 + x - 7 = 5
c) x2 + 3x - 6 = -8
d) x(x + 3) - 40 = 0
e) 4 + x (x - 4) = x
f) x(x + 5) - 2x = 28​

Soluções para a tarefa

Respondido por Usuário anônimo
1

Resposta:

a) x1 = 5 ; x2 = \frac{-3}{2}

b) x1 = 3 ; x2 = -4

c) x1 = -2 ; x2 = -1

d) x1 = -8 ; x2 = 5

e) x1 = 4 ; x2 = 1

f) x1 = 4 ; x2 = -7

Explicação passo-a-passo:

a)

2x^{2}  - 7x = 15\\\\2x^{2}  - 7x - 15 = 0\\\\delta = (-7)^{2} - (4 . 2 . -15)\\\\delta = 49 + 120\\\\delta = 169\\\\x = \frac{-(-7) +/- \sqrt{169} }{2 . 2}  \\\\x = \frac{7 +/- 13}{4} \\\\x1 = \frac{7 + 13}{4} =  \frac{20}{4}  = 5\\\\x2 = \frac{7 - 13}{4} = \frac{-6}{4} = \frac{-3}{2}

b)

x^{2}  + x - 7 = 5\\\\x^{2} + x - 7 - 5 = 0\\\\x^{2}  + x - 12 = 0\\\\delta = 1^{2} - (4 . 1 . -12)\\\\delta = 1 + 48\\\\delta = 49\\\\x = \frac{-1 +/- \sqrt{49} }{2 . 1} \\\\x = \frac{-1 +/ 7}{2} \\\\x1 = \frac{-1 +7}{2}  = 3\\\\x2 = \frac{-1 - 7}{2} = -4

c)

x^{2}  + 3x - 6 = -8\\\\x^{2} + 3x - 6 + 8 = 0\\\\x^{2}  + 3x + 2 = 0\\\\delta = 3^{2} - (4 . 1 . 2)\\\\delta = 9 - 8\\\\delta = 1\\\\x = \frac{-3 +/- \sqrt{1} }{2 . 1}  \\\\x = \frac{-3 +/ 1}{2} \\\\x1 = \frac{-3 - 1 }{2} = -2\\\\x2 = \frac{-3 + 1}{2}  = -1

d)

x (x + 3) - 40 = 0\\\\x^{2}  + 3x - 40 = 0\\\\delta = 3^{2} - (4 . 1 . -40)\\\\delta = 9 + 160\\\\delta = 169\\\\x = \frac{-3 +/- \sqrt{169} }{2 . 1}\\\\x = \frac{-3 +/- 13}{2}  \\\\x1 = \frac{-3 - 13}{2} = -8\\\\x2 = \frac{-3 + 13}{2} = 5

e)

4 + x (x - 4) = x\\\\4 + x^{2}  - 4x - x = 0\\\\x^{2}  - 5x + 4 = 0\\\\delta = (-5)^{2} - (4 . 1 . 4)\\\\delta = 25 - 16\\\\delta = 9\\\\x = \frac{-(-5) +/- \sqrt{9} }{2 . 1}  \\\\x = \frac{5 +/- 3}{2}\\\\x1 = \frac{5 + 3}{2} = 4\\\\x2 = \frac{5 - 3}{2} = 1

f)

x (x + 5) - 2x = 28\\\\x^{2}  + 5x - 2x - 28 = 0\\\\x^{2}  +3x - 28 = 0\\\\delta = 3^{2} - (4 . 1 . -28)\\\\delta = 9 + 112\\\\delta = 121\\\\x = \frac{-3 +/- \sqrt{121} }{2 . 1} \\\\x = \frac{-3 +/- 11}{2} \\\\x1 = \frac{-3 + 11}{2} = 4\\\\x2 = \frac{-3 - 11}{2}   = -7

Perguntas interessantes