Question

система 1/x - 1/y = -4/5   x-y = 4

Answer 1

Y - X XY = - 45

5*(Y-X) = - 4XY

5Y - 5X = - 4XY

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

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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

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X = 4 + Y

X1 = 4 - 5 = - 1

X2 = 4 + 1 = 5

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Ответ   X1 = - 1    Y1 = - 5

            X2 = 5      Y2 = 1