Question

Resolva essa equação usando a formula de Bhaskara:

a) (-2, -5/2)
b) (-2, +5/2)
c) (2, 5/2)
d) (2, -5/2)

Answer 1

Resposta:

alternativa d

Explicação passo-a-passo:

$\frac{x(3 - 4x)}{6} - \frac{5}{9} - \frac{x - {x}^{2} }{3} = \frac{x(1 - 4x)}{9}$

$\frac{3x - 4 {x}^{2} }{6} - \frac{5}{9} - \frac{x - {x}^{2} }{3} = \frac{x - 4 {x}^{2} }{9}$

$\frac{3(3x - 4 {x}^{2}) -( 2 \times 5) - 6(x - {x}^{2}) = 2(x - 4 {x}^{2}) }{18}$

$9x - 12 {x}^{2} - 10 - 6x + 6 {x}^{2} = 2x - 8 {x}^{2} \\ 9x - 12 {x}^{2} - 10 - 6x + 6 {x}^{2} - 2x + 8 {x}^{2} = 0 \\ 2 {x}^{2} + x - 10 = 0$

$x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a}$

$x = \frac{ - 1 + - \sqrt{ {1}^{2} - 4 \times 2 \times ( - 10) } }{2 \times 2}$

$x = \frac{ - 1 + - \sqrt{1 + 80} }{4}$

$x = \frac{ - 1 + - \sqrt{81} }{4}$

$x1 = \frac{ - 1 + 9}{4} = \frac{8}{4} = 2$

$x2 = \frac{ - 1 - 9}{4} = - \frac{ 10}{4} = - \frac{5}{2}$