If  
x
y
  +  
y
x
  = 1 (x,y ≠ 0), find the value of x3 + y3.


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Answer:

0

Step by Step Explanation:
  1. It is given that,  
    x
    y
      +  
    y
    x
      = 1 (x,y ≠ 0)
    ⇒  
    x2 + y2
    xy
      = 1
    ⇒ x2 + y2 = xy
    ⇒ x2 + y2 - xy = 0 ------(1)
  2. Now, x3 + y3 can be written as:
    (x + y)(x2 - xy + y2)
    = (x + y)(0) ......(Using equation (1))
    = 0
  3. Therefore, the value of x3 + y3 is 0.

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