Question

Resolva as equações.

a) x²/3 + 3 - 2x = 0
b) 2x² - 3x/2 + 1/4 = 0
c) x + 1/2 - x² + 1/3 = 0
d) x²/2 - 1/5 = 3x - 1/5

Conta pfvr.

Answer 1

$a) \frac{ {x}^{2} }{3} + 3 - 2x = 0 \\ 3 {x}^{2} + 9 - 6x = 0 \\ delta = 81 - 4 \times 3 \times ( - 6) = 9 \\ x = - 1 \: ou \: x = - 2$
$b)4 \times2 {x}^{2} - \frac{3x}{2} \times 4 + \frac{1}{4} \times 4 = 0 \\ 8 {x}^{2} - 6x + 1 = 0 \\ delta = 4 \\ x = \frac{1}{2} \: ou \: x = \frac{1}{4}$
$c)x + \frac{1}{2} - {x}^{2} + \frac{1}{3} = 0 \\ - {x}^{2} + x + \frac{5}{6} = 0 \\ - 6 {x}^{2} + 6x + 5 = 0 \\ delta = 156 \\ x = \frac{6 + \sqrt{156} }{12} ou \: x = \frac{6 - \sqrt{156} }{12}$
$d) \frac{ {x}^{2} }{2} - \frac{1}{5} = 3x - \frac{1}{5} \\ {x}^{2} - 6x = 0 \\ x(x - 6) = 0 \\ x = 0 \: ou \: x = 6$