Question

resolva a equação 5y + (y+2)² =3y(y+2) + y, sendo U = R​

Answer 1

Oie, Td Bom?!

$5y + (y + 2) {}^{2} = 3y \: . \: (y + 2) + y$

$5y + y {}^{2} + 4y + 4 = 3y {}^{2} + 6y + y$

$9y + y {}^{2} + 4 = 3y {}^{2} + 7y$

$9y + y {}^{2} + 4 - 3y {}^{2} - 7y = 0$

$2y - 2 y {}^{2} + 4 = 0$

$- 2y {}^{2} + 2y + 4 = 0$

$y {}^{2} - y - 2 = 0$

• Coeficientes:

$a = 1 \: , \: b = - 1 \: ,\: c = - 2$

• Fórmula resolutiva:

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

$y = \frac{ - ( - 1)± \sqrt{( - 1) {}^{2} - 4 \:. \:1 \: . \: ( - 2) } }{2 \: . \: 1}$

$y = \frac{1± \sqrt{1 + 8} }{2}$

$y = \frac{1 ± \sqrt{9} }{2}$

$y = \frac{1± 3 }{2}$

$⇒y = \frac{1 + 3}{2} = \frac{4}{2} = 2$

$⇒y = \frac{1 - 3}{2} = \frac{ - 2}{2} = - 1$

$S = \left \{ - 1 \: , \: 2 \right \}$

Att. Makaveli1996