Question

Решить систему уравнений:
1)7/x+y/5=28
2)x/7+5/y=5

Answer 1

Замена 7/x = a; y/5 = b
{ a + b = 28
{ 1/a + 1/b = 5
Подставляем 1 уравнение во 2
{ b = 28 - a
{ 1/a + 1/(28-a) = 5
28 - a + a = 5a(28 - a)
28 + 5a^2 - 140a = 0
D/4 = 70^2 - 5*28 = 4900 - 140 = 4760
a1 = (70 - √4760)/5; b1 = 28 - a1 = (70 + √4760)/5
a2 = (70 + √4760)/5; b2 = 28 - a2 = (70 - √4760)/5
1) 7/x = a1 = (70-√4760)/5; x1 = 7*5/(70-√4760) = 35(70+√4760)/140 =
= (70+√4760)/4
y/5 = b1 = (70+√4760)/5; y1 = (70+√4760)
2) Аналогично
7/x = a2 = (70+√4760)/5; x2 = 7*5/(70+√4760) = (70-√4760)/4
y/5 = b2 = (70-√4760)/5; y2 = (70-√4760)

Answer 2

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