Question

calcular as raizes, equaç/2 grau
a) x² + 12x + 36 = 16
b) 3x² + 18x = 0
c) 4x² - 100 = 0
d) (-2x +1)² = 49

Preciso de ajuda nessas pfv

Answer 1

a) x^2+12x+36-16
x^2+12x+20=0
a=1, b=12, c=20

∆= b^2-4ac=12^2-4.1.20=144-80=64
-b+-✓64/2/a= -12+-8/2.1= -12+-/2
x= -12+8/2=-4/2=-2
x=-12-8/2=-20/2=-10

S: x'=-10 e x''=-2.

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B)a=3, b=18, c=0

∆= b^2-4ac=18^2-4.10= 324-0=324
-b+-✓∆/2a= -18+-18/2.3= -18+-18/6
x=-18+18/6= 0/6=0
x=-18-18/6= -36/6=-6

S: x'=0 e x''=-6.

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c) a=3, b=0, c=-100
∆=b^2-4ac= 0^2-4.4.(-100)= 1600
-b+-✓∆/2a= 0+-✓1600/2.4= +-40/8=
x=40/8= 5
x=-40/8= -5
S: x'=5 e x''=-5.
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d)-2x+1=+-49
-2x+1=+-7
separar a equação em dois casos possíveis:
-2x+1= 7
-2x+1= -7

Primeiro caso:
-2x+1= 7
-2x= 7-1
-2x= 6
x= -6/2
x= -3
Segundo caso:
-2x+1= -7
-2x= -7-1
-2x= -8
x= -8/-2
x= 4.

S: x'= -3 e x''= 4.