Question

Sendo y' e y" raízes da operação, y² -5y -24, calcule:
a) 9 . y" / 9 . y' =
b) ( y" )³ - ( y' )³ =
c) y' / 3 - y" / 2 =

Answer 1

Resposta:

Olá! ^-^

$y^2- 5y-24=0$

Sabendo que:

• a= 1
• b= -5
• c= -24

Calculando o Δ:

$delta= b^2-4.a.c\\delta= (-5)^2- 4. (1). (-24)\\delta= 25+ 96\\delta= 121$

Achando as raízes:

$y'= -b+\sqrt{delta} / 2.a\\y'= 5+ \sqrt{121} / 2.1\\y'= 5+11/2\\y'= 16/2\\y'= 8$

$y"= -b-\sqrt{delta} / 2.a\\y"= 5-\sqrt{121} / 2.1\\y"= 5-11/2\\y"= -6/2\\y"= -3$

S= {8, -3}

Dessa forma:

a) $9.y"/ 9.y'= 9.(-3)/ 9.8= -27/ 72 (:9)= -3/ 8$

b) $(y")^3- (y')^3= (-3)^3- (8)^3= -27-512= -539$

c) $y'/3- y"/2= \frac{8}{3} - \frac{-3}{2} = \frac{8}{3}+ \frac{3}{2} = \frac{16}{6} +\frac{9}{6} =\frac{25}{6}$

Espero ter ajudado! <3