Question

Найдите значение дроби 3y2-2y/6-7y-3y2 при y=6

Answer 1

$\\ 6 - 7y - 3 {y}^{2} = 0\\ 3 {y }^{2} + 7y - 6 = 0 \\ D = {b}^{2} - 4ac = \\ = {7}^{2} - 4 \cdot3 \cdot( - 6) = 121 \\x_1,_2= \frac{ - 7±11 }{6} \\ x_1 = \frac{2}{3}\\ x_2=- 3 \\ 3 {y }^{2} + 7y - 6 =3(y - \frac{2}{3} )(y + 3)\\ = \frac{3 {y}^{2} -2 y}{6 - 7y - 3 {y}^{2} } = - \frac{3 {y}^{2} -2 y}{3 {y}^{2} + 7y - 6} = \\ = - \frac{3y (y - \frac{2}{3}) }{ 3(y - \frac{2}{3})(y + 3) } = - \frac{y}{y + 3} \\$
при у=6

$= - \frac{6}{6 + 3} = - \frac{6}{9} = - \frac{2}{3}$