Yahoo Answers: Answers and Comments for Find (x/y)^3? [Mathematics]
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enUS
Sat, 12 Oct 2019 09:37:04 +0000
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Yahoo Answers: Answers and Comments for Find (x/y)^3? [Mathematics]
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From 冷眼旁觀: (1/x) + (1/y) = 1/(x + y)
[(1/x) + (1/y)] * x ...
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Sat, 12 Oct 2019 11:39:42 +0000
(1/x) + (1/y) = 1/(x + y)
[(1/x) + (1/y)] * x = [1/(x + y)] * x
1 + (x/y) = x/(x + y)
(x/y) + 1 = (x/y)/[(x + y)/y]
(x/y) + 1 = (x/y)/[(x/y) + 1]
Put a = x/y:
a + 1 = a/(a + 1)
(a + 1)² = a
a² + 2a +1 = a
a² + a + 1 = 0
(a  1)(a² + a + 1) = 0
a³  1 = 0
a³ = 1
Hence, (x/y)³ = 1

From Φ² = Φ+1: 1/x + 1/y = 1/(x+y)
(x+y)/(xy) = 1/(x+y)
(x+y)...
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Sat, 12 Oct 2019 11:40:55 +0000
1/x + 1/y = 1/(x+y)
(x+y)/(xy) = 1/(x+y)
(x+y)² = xy
x² + xy + y² = 0
x = y/2 ± √(y²4y²)/2 = y/2 ± i y√3/2
x/y = 1/2 ± i √3/2
(x/y)³ = (½ ± i ½√3)³ = 1

From JOHN: Set u = x/y
x(1/x + 1/y) = x/(x + y)
1 + u = 1...
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Sat, 12 Oct 2019 11:55:23 +0000
Set u = x/y
x(1/x + 1/y) = x/(x + y)
1 + u = 1/(1 + 1/u) = u/(1 + u)
(u + 1)² = u
u² + 2u + 1 = u
u² + u + 1 = 0
u³  1 = (u  1)(u² + u + 1) = 0
u³ = (x/y)³ = 1.

From az_lender: xy + y^2 + x^2 + xy = xy =>
x^2 + xy + y^2 ...
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Sat, 12 Oct 2019 11:43:10 +0000
xy + y^2 + x^2 + xy = xy =>
x^2 + xy + y^2 = 0 =>
x = y/2 +/ (yi/2)*sqrt(3) =>
x/y = 1/2 +/ i*sqrt(3)/2 =>
(x/y)^3 = 1.