1996 AIME Problems/Problem 8
Problem
The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers with
is the harmonic mean of
and
equal to
?
Solution
The harmonic mean of and
is equal to
, so we have
, and
.
has
factors, one of which is the square root. Since $x\< y$ (Error compiling LaTeX. Unknown error_msg), the answer is half of the rest of them, which is
.
See also
1996 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |