Find (x/y)^3?

If 1/x + 1/y = 1/(x+y) find (x/y)^3

4 Answers

Relevance
  • 2 months ago
    Best answer

    (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

  • JOHN
    Lv 7
    2 months ago

    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.

  • 2 months ago

    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.

  • 2 months ago

    1/x + 1/y = 1/(x+y)

    (x+y)/(xy) = 1/(x+y)

    (x+y)² = xy

    x² + xy + y² = 0

    x = -y/2 ± √(y²-4y²)/2 = -y/2 ± i y√3/2

    x/y = -1/2 ± i √3/2

    (x/y)³ = (-½ ± i ½√3)³ = 1

    • BigBird2 months agoReport

      {1e^[(+/-)(2/3)(pi)] }^3 =e^[2(pi)] = +1

Still have questions? Get answers by asking now.