Question

PRA AGORA - matematica (20 pontos)

Answer 1

Resposta:

a) y = 1 (y < x)

b) x1 = 4; x2 = - 5

c) x1 = 6; y1 = 1; x2 = 3; y2 = 4 (6, 1),(3, 4)

d) Total de pessoas (x) = 28

Explicação passo-a-passo:

a)

x + y = 6 => y = 6 - x

x² - y² = 24

x² - (6 - x)² = 24

x² - (6² - 2.6.x + (-x)²) = 24

x² - (36 - 12x + x²) = 24

x² - 36 + 12x - x² = 24

12x = 24 + 36

12x = 60

x = 60/12 = 5

y = 6 - 5 = 1

b)

x² + (x + 1)² = 41

x² + x² + 2x + 1 = 41

2x² + 2x - 40 = 0 (÷2)

x² + x - 20 = 0

∆ = 1² + 4.1.20 = 1 + 80 = 81

√∆ = √81 = 9

x = (- 1 ± 9)/2

x1 = 8/2 = 4

x2 = - 10/2 = - 5

c)

x + y = 7 => y = 7 - x

x + √y = 5

√y = (5 - x)

(√y)² = (5 - x)²

y = 5² - 2.5.x + x²

7 - x = 25 - 10x + x²

x² - 10x + x + 25 - 7 = 0

x² - 9x + 18 = 0

√∆ = √(9² - 4.18) = √81 - 72 = √9

√∆ = 3

x = (9 ± 3)/2

x1 = 12/2 = 6

x2 = 6/2 = 3

y1 = 7 - x1 = 7 - 6 = 1

y2 = 7 - x2 = 7 - 3 = 4

(x1, y1) = (6, 1)

(x2, y2) = (3, 4)

d)

p.x = 280

p = 280/x

(p + 12).(x - 3) = 280

(280/x + 12).(x - 3) = 280

(280 + 12x).(x - 3) = 280x

280x + 12x² - 3.280 - 3.12x = 280x

12x² - 36x - 840 = 0 (÷12)

x² - 3x - 70 = 0

√∆ = √(3² + 4.70) = √(9 + 280) = √289

√∆ = 17

x = (3 ± 17)/2

x1 = 20/2 = 10

x2 = - 14/2 = - 7

verificação:

p.x = 280

10p = 280

P = $28/pessoa

(p + 12).(x - 3) = 280

(28 + 12).(10 - 3) =

40 × 7 = $280