система 1/x - 1/y = - 4/5 x-y = 4

Question

Алгебра

Урбана

9 июля, 12:12

система 1/x - 1/y = - 4/5 x-y = 4

+1

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Аэлита · Answer 1

Y - X / XY = - 4/5

5 * (Y-X) = - 4XY

5Y - 5X = - 4XY

...

X - Y = 4 - - - > X = 4 + Y

...

5Y - 5 * (4+Y) = - 4 * (4+Y) * Y

5Y - 20 - 5Y = ( - 16 - 4Y) * Y

- 20 = - 16Y - 4Y^2

-4Y^2 - 16Y + 20 = 0

4 * (-Y^2 - 4Y + 5) = 0

D = 16 - 4 * (-1) * 5 = 16 + 20 = 36

V D = 6

Y1 = 4 + 6 / - 2 = 10/-2 = - 5

Y2 = 4 - 6 / - 2 = - 2/-2 = 1

...

X = 4 + Y

X1 = 4 - 5 = - 1

X2 = 4 + 1 = 5

...

Ответ X1 = - 1 Y1 = - 5

X2 = 5 Y2 = 1