Question

Resolva as equações
A) 3x²+ 15x =0
B)x²-100=0
C) (x+3)²= 12- x²

D)x(x-18)
________ = -9
9

É) x²-1 -2x = - x -1
_______ ______
3 2
F) x(x-2) + 3= 6 (x-2)

Answer 1

A) 3x^2 + 15x = 0
3x( x + 5 ) = 0
3x=0》 x =0/3》x = 0
x + 5 = 0》x = -5

B) x^2 - 100 =0
x = +,- \/100
x = +,- 10

C) ( x + 3 )^2 = 12 - x^2
(x)^2 + 2(x)(3) + (3)^2 = 12 - x^2
x^2 + 6x + 9 = 12 - x^2
x^2 + x^2 + 6x +9 - 12 = 0
2x^2 + 6x - 3 =0
a= 2. b= 6 c= -3
delta = b^2 - 4 a c
delta = (6)^2 - 4 (2)(-3)
delta = 36 - 8(-3)
delta = 36 +24
delta = 60
X = - b+,- \/delta /2a
X = -(6)+,- \/60/2(2)
X = -6+,- 7,74/4
X1 = - 6 + 7,74/4》X1 = 1,74/4》X1 =0,435
X2 = -6 -7,74 /4》 X2 = -13,74/4》X2=-3,435

D) x ( x -18 ) = -9
__------------
_____9
x ( x - 18 ) = -9 (9)
x^2 - 18x = -81
x^2 - 18x + 81 =0
( x - 9 ) ( x - 9 ) = 0
x1 - 9 = 0》x1 = 9
x2 - 9 = 0》 x2 = 9
x1 =x2

E) x^2 - 1 - 2x = - x - 1
__---------------__--------
_____3________2

2 ( x^2 - 1 - 2x ) = 3 (- x - 1 )
2x^2 - 2 - 4x = -3x - 3
2x^2 -4x + 3x - 2 + 3 = 0
2x^2 - x + 1 = 0
( 2x - 1 ) ( x - 1 ) =0
2x - 1 = 0》2x = 1》x = 1/2
x - 1 = 0》x = 1

F) x( x - 2 ) + 3 = 6 ( x - 2 )
x^2 - 2x + 3 = 6x - 12
x^2 - 2x - 6x +3 + 12 = 0
x^2 - 8x + 15 = 0
( x - 5 ) ( x - 3 ) = 0
x - 5 = 0》x = 5
x - 3 = 0》 x = 3