Question

Escreva a equação na forma reduzida. Depois a resolva

Answer 1

Explicação passo-a-passo:

b)

$\sf \dfrac{3y+1}{2}=\dfrac{y^2-1}{3}$

$\sf 2\cdot(y^2-1)=3\cdot(3y+1)$

$\sf 2y^2-2=9y+3$

$\sf 2y^2-9y-2-3=0$

$\sf \red{2y^2-9y-5=0}~\Rightarrow~$ forma reduzida

$\sf \Delta=(-9)^2-4\cdot2\cdot(-5)$

$\sf \Delta=81+40$

$\sf \Delta=121$

$\sf y=\dfrac{-(-9)\pm\sqrt{121}}{2\cdot2}=\dfrac{9\pm11}{4}$

$\sf y'=\dfrac{9+11}{4}~\Rightarrow~y'=\dfrac{20}{4}~\Rightarrow~\red{y'=5}$

$\sf y"=\dfrac{9-11}{4}~\Rightarrow~y"=\dfrac{-2}{4}~\Rightarrow~\red{y"=\dfrac{-1}{2}}$