Question

Resolva as duas equações de 2 grau

Answer 1

j)
{9[(x+3)*(x+3)]}/2=18
{9[x²+3x+3x+9]}/2=18
{9x²+27x+27x+81}/2=18
{9x²+54x+81}/2=18
9x²+54x+81=18*2
9x²+54x+81=36
9x²+54x+81-36=0
---> 9x²+54x+45=0
a=9,b=54,c=45

∆=b²-4ac
∆=54²-4*9*45
∆=2916-1620
∆=1296

x=(-b±√∆)/2a
x=(-54±√1296)/2*9
x=(-54±36)/18

x'=(-54+36)/18
x'=-18/18
x'=-1

x"=(-54-36)/18
x"= -90/18
x"= -5


k)
(y/2)+(1-y/2)-(2y²/3)=-1
MMC entre 2,2,3=6
[(6/2)*y+(6/2)*1-y - (6/3)*2y²]/6=-1
[3*y+3*1-3*y-2*2y²]/6=-1
[3y+3-3y-4y²]/6=-1
[-4y²+3]/6=-1
-4y²+3=-1*6
-4y²+3=-6
-4y²=-6+3
-4y²=-3
y²=-3/-4 ou 3/4
y=√-3/4