Lista de exercícios 2 Resolução

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UNIVERSIDADE FEDERAL DE MINAS GERAIS
ESCOLA DE ENFERMAGEM
CURSO DE GESTÃO EM SERVIÇOS DE SAÚDE
Lista de Exercícios 2 
Disciplina: Cálculo aplicado à Saúde 
1. Sendo A = 6x³ + 5x² – 8x + 15, B = 2x³ – 6x² – 9x + 10 e C = x³ + 7x² + 9x + 20. Resolva:
 a) A + B + C
= 6x³ + 5x² – 8x + 15 + 2x³ – 6x² – 9x + 10 + x³ + 7x² + 9x + 20 
= (6x³+ 2x³+ x³) + ( + 5x²– 6x²+ 7x²) + (– 8x– 9x+ 9x) + (+ 15+ 10+ 20)
= 9x³ + 6x² - 8x +45
 b) A – B – C
=( 6x³ + 5x² – 8x + 15) – (+ 2x³ – 6x² – 9x + 10) – ( + x³ + 7x² + 9x + 20)
=( 6x³ + 5x² – 8x + 15) + (- 2x³ + 6x² + 9x - 10) + ( - x³ - 7x² - 9x - 20)
= (6x³ - 2x³ - x³) + ( + 5x² + 6x² - 7x²) + (– 8x + 9x - 9x) + (+ 15 – 10 - 20)
= 3x³ + 4x² -8x -15
 c) A – C
=( 6x³ + 5x² – 8x + 15) - ( + x³ + 7x² + 9x + 20)
= 6x³ + 5x² – 8x + 15 - x³ - 7x² - 9x - 20
=5x³ -2x² -17x -5
 d) B – A
=(+ 2x³ – 6x² – 9x + 10) - ( 6x³ + 5x² – 8x + 15)
=(+ 2x³ – 6x² – 9x + 10) + ( - 6x³ - 5x² + 8x - 15)
= - 4x³ -11x² -x -5
 e) A + C
=( 6x³ + 5x² – 8x + 15) + ( + x³ + 7x² + 9x + 20)
= 7x³ + 12x² +x +35
Questão 2
1. (4b + 3c - a) + (4a – 3b – 2c) = 
4b - 3b + 3c - 2c – a + 4a = 
b + c + 3a
2. (5ab – 3c + 4d) + (-2d + 3c – 4ab)
5ab – 4ab -3c + 3c + 4d – 2d =
ab + 2d
3. (xy - 3x2 + 1) + (3 + 5x2 – 3xy)
xy – 3xy - 3x2 + 5x2 +1 + 3 = 
-2xy + 2x2 + 4
4. +
 =
 
5. (5xy – x3 + 4y) + (5 + 2x3 - 4y - 6xy)
5xy – 6xy – x3 + 2x3 + 4y – 4y + 5 =
-xy + x3 + 5
6. (10x + 20y) – (5x + 15y)
10x – 5x + 20y – 15y =
5x + 5y
7. (xy3 – 2xy + 1) – (4xy + 5 + 2xy3)
xy3 - 2xy3 – 2xy – 4xy + 1 – 5 =
-xy3 – 6xy – 4
8. (x2 + 2xy + 3y2) – (x2 – 2xy + 3y2)
x2 – x2 + 2xy + 2xy + 3y2 - 3y2 = 
4xy
9. (-x3 + 2xy + 4) – (2x3 + 2xy + 8)
-x3 - 2x3 + 2xy – 2xy + 4 – 8 =
-3x3 – 4
10. +
 =
11. (5a)(-7c) = 
-35ac
12. (4a2b)(-7ab2)
-28a3b3
13. (x + y2 + 4) (x + 1) 
x2 + x + xy2 + y2 + 4x + 4 =
x2 + 5x + xy2 + y2 + 4
14. (4x – 3y)(4x + 3y)
16x2 + 12xy – 12xy – 9y2 =
16x2 – 9y2
15. (x + 3) (x + 3) = (x+3)2
X2 + 3x + 3x + 9 =	
X2 + 6x + 9 =
16. (8x2) / (4x2) =
2
17. (1xy) / (4xy2) =
18. (3a2b4) / (5a4b2)
19. (5x2y3 + 4x4y – 3xy2) / (2xy)
20. 
Questão 3
a) a² - 4a +4 – 2a -4 = a² -6a
b) y² +10y +25 – y² -10y= 25
c) a² +2ab +b² + a² -2b +b² = 2a² + 2b² 
d) x² -6x +9 +x² +6x +9 = 2x² +18
e) x² - y² + x² +2xy +y² - 2xy = 2x²
Questão 4
a) 4x² +4x+ 1 + 4x² - 4x +1 = 8x² +2
b)3*( y4 – 2y² +1) +2* (4y² +8y +4) = 3y4 – 6y² +3 +8y² +16y +8= 3y4 +2y² +16y +11
c) 2x³y -4xy +3x² -6 – (x² -2x +1) = 2x³y -4xy +3x² -6 -x² +2x -1 = 2x³y -4xy +2x² -7+2x 
d) 4x² +4x +1 + 2x*( x² -2x +1) = 4x² +4x +1 + 2x³-4x² +2x= +6x +1 + 2x³
e) a²b² +2ab+1 + a²b² + 2ab = 2a²b² +4ab +1
f) 16a²y² -8ay +1 -4*(a²y² - 2ay +1) = 16a²y² -8ay +1 -4a²y² + 8ay -4 = 12a²y² -3 
Questão 5
1- 2x( 1 +2) = 2x.3 = 6x
2- 3(x-3y+4)
3- xy( 4 -3xy +10x²)
p + pin
4- p(1+in)
5- 2x( 5x – 6)
6- (1+i)²
7- (x+
8- (2x+3y)²
9- (x+)²
10- (2x² +1)²
Questão 6
a) 7a( 4b – 3c -1)
b) 3x(2x – 5) – 2y(2x -5) = (2x-5)(3x-2y)
c) (x -
d) (a²b – y) (a²b +y)
e) 5( x² - 8x + 16) = 5 (x – 4)²
f) (4y² - 5)2
g) 3x( x² +6xy +9y²) = 3x (x + 3y)2
ax2 + bx + c = a(x – x’)(x – x’’)
h) x2 + 9x + 14
▲= 81 – 56 = 25
x = (-9 ± 5)/2
x’ = -7
x’’ = -2
x2 + 9x + 14 = 1[x – (-7)][x – (-2)] = (x +7) (x + 2)
x2 + 9x + 14 = (x +7) (x + 2)
Questão 7
1. =
 
2. 
−4
3. 
4. 
5. 
+3
6. 
7. 
8.