Respostas
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