contestada

The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs $(x,y)$ of positive integers is the harmonic mean of $x$ and $y$ equal to $20$

Respuesta :

sqdancefan

Answer:

  9 ordered pairs

Step-by-step explanation:

The requirement that the harmonic mean of two positive integers be 20 places a restriction on what those integers may be.

  20 = 2/(1/x +1/y)

  y = 10x/(x -10)

Integer values of x that produce integer values of y are ...

  x ∈ {11, 12, 14, 15, 20, 30, 35, 60, 110}

The corresponding 9 ordered pairs are ...

  (11, 110), (12, 60), (14, 35), (15, 30), (20, 20), (30, 15), (35, 14), (60, 12), (110, 11)

Otras preguntas