1/x+1/y=5 1/x в квадрате+1/y в квадрате = 13

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Алгебра

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12 марта, 06:43

1/x+1/y=5 1/x в квадрате+1/y в квадрате = 13

+4

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Матрона · Answer 1

1/x+1/y=5, (x+y) / xy=5, x+y=5xy, 5xy-x=y, x (5y-1) = y, x=y / (5y-1), x^2=y^2 / (25y^2-10y+1).

1/x^2+1/y^2=13, (x^2+y^2) / x^2y^2=13, x^2+y^2=13x^2y^2.

y^2 / (25y^2-10y+1) + y^2=13y^4 / (25y^2-10y+1), y^2 * (25y^2-10y+1) + y^2=13y^4, 25y^4-10y^3+y^2+y^2=13y^4, 12y^4-10y^3+2y^2=0, 6y^2-5y+1=0, D=25-24=1, y1 = (5-1) / 12=1/3, y2 = (5+1) / 12=1/2.

x1 = (1/3) / (5/3-1) = (1/3) / (2/3) = 1/2, x2 = (1/2) / (5/2-1) = (1/2) / (3/2) = 1/3.