Question

Resolva as equações :

a) (x-1)²=7+x
b) (x-2)²-x=1
c) x²/4 - x/3 +1/9=0
d) x²-3= x-3/6

Answer 1

a) ( x - 1 )^2 = 7 + x
(x)^2 - 2(x)(1) + (1) = 7 + x
x^2 - 2x +1 = 7 + x
x^2 - 2x - x + 1 - 7 = 0
x^2 - 3x -6 = 0
FORMULA DE BASKARA
a=1. b=-3 c=-6
Delta = b^2 - 4 a c
Delta = (-3)^2 - 4(1)(-6)
Delta = 9 - 4(-6)
Delta = 9 + 24
Delta = 33
X = - b +,- \/Delta/2a
X = - (-3) +,- \/33/2(1)
X = 3 +,- 5,74/2
X1 = 3 + 5,74/2》X1 =8,74/2》X1 = 4,37
X2 = 3 - 5,74/2》X2 = -2,74/2》X2 = -1,37

b) ( x - 2 )^2 - x = 1
[(x)^2 - 2(x)(2) + (2)^2] - x = 1
( x^2 - 4x + 4) - x = 1
x^2 - 4x - x + 4 - 1 = 0
x^2 - 4x + 3 = 0
( x - 3 ) ( x - 1 ) = 0
x1 - 3 = 0》x1 = 3
x2 - 1 = 0》x2 = 1

c) x^2/4 - x/3 + 1/9 = 0 ( m.m.c = 36 )
9x^2 - 12x + 4 /36=0
9x^2 - 12x + 4 = 36
9x^2 - 12x + 4 - 36 = 0
9x^2 - 12x - 32 = 0
FORMULA DE BASKARA
a=9. b= -12 c= -32
delta = b^2 - 4 a c
delta = (-12)^2 - 4(9)(-32)
delta = 144 - 36(-32)
delta = 144 + 1152
delta = 1296
x = - b +,- \/delta/2a
x = - (-12) +,- \/1296/2(9)
x = 12 +,- 36/18
x1 = 12 + 36/18》x1 = 48/18》x1 = 2,66
x2 = 12 - 36 /18》x2 = -24/18》x2 = -1,33

d) x^2 - 3 = x - 3/6
x^2 - 3 = 6x - 3/6
6(x^2 - 3 ) = 6x - 3
6x^2 - 18 = 6x - 3
6x^2 - 6x - 18 + 3 = 0
6x^2 - 6x - 15 = 0
FORMULA DE BASKARA
a=6. b= -6 c= -15
delta = b^2 4 a c
delta = (-6)^2 - 4(6)(-15)
delta = 36 - 24(-15)
delta = 36 + 360
delta = 396
x = - b +,- \/delta/2a
x = - (-6)+,- \/396/2(6)
x = 6 +,- 19,89/12
x1 = 6 + 19,89/12》x1 = 25,89/12》
x1 = 2,15
x2 = 6-19,89/12》x2 = -13,89/12》
x2 = -1,15