MATHEMATICS WORKS by Bruna Serpa

bruna_serpa — 2018-10-31 10:59:51 UTC

Bruna - 26; 27; 31; propostas 2,3
Carolina- 30; 32;
Nuno- 29
Rodrigo- 28

EX.: 26 (pg.110)

bruna_serpa — 2018-10-31 11:06:14 UTC

26.1 P(x) = (-x³+ 3x -2) : (x-1)
P(1)= -(1)³+ 3.(1) -2
= -1 + 3 -2= 0
R=0
26.2 P(x) = (-x³+ 3x -2) : (x+1)
P(-1)=-(-1)³+ 3.(-1) -2
= 1 -5= -4
R=0

26.3 P(x) = (-5x⁴-1/2x +3) : (x)
X=0
P(0)= -5.(0)⁴-(1/2).0 +3
= 0 - 0 +3 =3
R=3
26.4 P(x) = (2x³-x²+x) : (2x-1)

2x -1 =0 <=> 2x =1 <=> x= 1/2

P(1/2)= 2.(1/2)³-(1/2)²+(1/2)
= (1/4) -(1/4) +(1/2)= 1/2
R=1/2

28.

rodrigo_marques_neves2003 — 2018-11-05 11:53:08 UTC

28.1 A(2)=x³-2x +1
=8-4+1
=5 R(2)=5

28.2 A(1/2)= 2x³ +x² +3
=2/8 + 1/4 + 3
=2/8 + 2/8 + 24/8
=24/8
R(1/2)= 3

28.3 A(1)=2x⁷⁸+x⁶⁵-x +1
=2-1+1+1
=3
R(1)=3

EX.: 27

bruna_serpa — 2018-11-05 16:50:43 UTC

K ∈ R
(2x³-5x²+kx -3) : (x-3)
R=0
x-3= 0 <=> x=3
P(3) = 2.(3)³-5.(3)²+k.3 +3
= 54 -45 +3k +3 = 9 +3k +3
= 12 +3k
3k = -12
<=> k= -12/3
<=> k= -4

Ex.: 31

bruna_serpa — 2018-11-05 17:18:58 UTC

P(x) = xⁿ⁺¹+2xⁿ-1
Q(x) = xⁿ⁺¹-2xⁿ+x^n-1
31.1 P(x) : (x+1)

n= par => n+1 = ímpar
x+1=0 <=> x= -1
P(-1) = -1ⁿ⁺¹+2.(-1)ⁿ-1
= -1 +2.1 -1
= -2 +2 = 0

31.2 P(x): (x+1) ;
R=-2
x=-1
n = ímpar => n+1 = par
P(-1) = -1ⁿ⁺¹+2.(-1)ⁿ-1
= 1 -2 -1 = -2

31.3 Q(x) = xⁿ⁺¹-2xⁿ+x^n-1
Q(x) : (x-1) ; R=0
x= 1 ;
n = ímpar => n+1 = par => n-1 = par
Q(1) = 1ⁿ⁺¹-2.1ⁿ+1^n-1= 1 -2 +1 = 0
n = par => n+1 = ímpar => n-1 = ímpar
Q(1) = 1ⁿ⁺¹-2.1ⁿ+1^n-1= 1 -2 + 1 = 0
31.4 Q(x) : (x+1) ; R /=0
x=-1
n= ímpar => n+1= par => n-1= par
Q(-1) = (-1)ⁿ⁺¹-2.(-1)ⁿ+ (-1)^n-1= 1 -2. (-1) +1 =
= 1 +2 +1 = 4
n = par => n+1 = ímpar => n-1 = ímpar
Q(-1) = (-1)ⁿ⁺¹-2.(-1)ⁿ+(-1)^n-1= -1 -2.1 -1 =
= -1 -2 -1 = -4

Pág.111(exer.29)

2018-11-06 21:52:22 UTC

29.
3X+3=0«=»X=-1
5X-5=0«=»X=1
P(-1)=2
P(1)=-3
SISTEMAS:
[a(-1)^2015]-[b(-1)^2000 +1]=2

[a(1)^2015]-[b(1)^2000 +1]=-3
-a-b+1=2
a-b+1=-3
-a-b=1
a-b=-4
-b+4-b=1
a=b-4
-2b=1-4
a=b-4
b=3/2
a=3/2-4/1(x4)
b=3/2
a=-5/2

Ex.30 (pág.112)

carolina_monteiro350 — 2018-11-07 17:04:12 UTC

30. x³-ax²-2x+b
1. P(2)=2³-a2²-4-b
=8-4a+4+b
=4a-4+b
b=4a-4
2. DÚVIDAS!!

Ex:32

carolina_monteiro350 — 2018-11-07 17:27:13 UTC

A(x)= 3x³+x²-12x-4
1.A(2)=3.2³+2²-12.2-4
=24-24=0

R:. 2 é raiz de A(x)

Ex: continuação do 32

carolina_monteiro350 — 2018-11-07 17:27:20 UTC

.3 Q(x)=3x²+7x+2
R=0
A(x)= (3x²+7x+2)(x-2)
=(3x²+7x+2)(x-2)=0
=3x²+7x+2=0 V x-2=0
x=2

CA:

carolina_monteiro350 — 2018-11-07 18:20:40 UTC

= x=-2 V x= -1\3 V x

Proposta 2 (pg.106)

bruna_serpa — 2018-11-07 19:16:40 UTC

2.1 D=?
D= d . q + r
D= (3x+1).(-2x²+5x) +3
D= -6x³+15x²-2x²+5x +3
D= -6x³+13x²+5x +3
2.2
D= (x²-3x+2).(2x³-x) +x-4
D= 2x⁵-x³-6x⁴+3x²+4x³-2x+x-4
D= 2x⁵-6x⁴-x³+4x³+3x²-2x+x-4
D= 2x⁵-6x⁴+3x³+3x²-x-4
2.3
D= (-x³+x-2)(-x²+2x) +x²-x
D= x⁵-x⁴-x³+2x²+2x²-4x+x²-x
D= x⁵-x⁴-x³+5x²-5x

Pag:125 ex:28

2018-11-12 18:47:26 UTC

28:1)
X^3 -4X=0
X=0 V X^2 -4=0
X=0 V X^2=4
X=0 V X=±2
X=0 V X=2 V X=-2
X(X+2)(X-2)=0

Continuação do 28.1

2018-11-17 17:29:30 UTC

Pág:142 Exer:19

2018-12-04 19:54:19 UTC

19.1)
A(4,0,0)
B(4,4,0)
D(0,4,4)
E(0,0,4)
F(4,0,0)
G(4,4,4)
0(0,0,0)

Pág:143 Exer:20

2018-12-04 20:01:24 UTC

20.1)3×3+2×2+1=14
20.2)
A(3,0,1)
B(2,2,2)
C(0,2,2)
D(1,1,3)
E(3,3,1)
F(1,2,2)

Pág:143 Exer:21

2018-12-04 20:07:00 UTC

21) RAIZ CÚBICA DE 27=3
A(0,3,0)
B(-3,0,0)
C(0,0,3)
D(-3,3,3)
E(3,-3,3)
F(3,-3,0)
G(6,-3,-3)
H(3,3,-3)
I(3,6,0)