Question

resolva com método de completa quadrado
a)2n^2+7n+6=0
b)9y^2-3y-2=0
c)3x^2+8x-3=0

RESOLVA POR FAVOR

Answer 1

Bom dia!

a)2n^2+7n+6=0

2n²+7n= -6
n²+7/2n= -3
n²+7/2n+(7/4)²= -3+(7/4)²
(n+7/4)²=1/16
n+7/4= ± 1/4

n+7/4= 1/4
n1= 7/4 - 1/4
n1= -3/2

n+7/4= -1/4
n2= -1/4 - 7/4
n2= -8/4
n2= -2



→n1= -3/2
→n2= -2

b)9y^2-3y-2=0

9y²-3=2
y²-1/3y=2/9
y²-1/3y+(1/6)²=2/9+(1/6)²
(y-1/6)²=1/4
y-1/6= ± 1/2

y-1/6= 1/2
y1= 1/2+1/6
y1= 2/3

y-1/6= -1/2
y2= -1/2 + 1/6
y2= -1/3

→Y1= 2/3
→Y2= -1/3

c)3x^2+8x-3=0

3x²+8=3
x²+8/3x=1
x²+8/3x+(8/6)²=1+(8/6)²
(x+8/6)²=25/9
(x+4/3)²=25/9
x+4/3= ±5/3

x+4/3= 5/3
x1= 5/3 - 4/3
x1= 1/3

x+4/3= -5/3
x2= -5/3 - 4/3
x2= -9/3
x2= -3

→X1= 1/3
→X2= -3

Espero ter ajudado!