1973 IMO Problems/Problem 3
Let and
be real numbers for which the equation
has at least one real solution. For all such pairs
, find the minimum value of
.
Solution
Substitute to change the original equation into
. This equation has solutions
. We also know that
. So,
Rearranging and squaring both sides,
So, .
Therefore, the smallest possible value of is
, when
and
.
Borrowed from http://www.cs.cornell.edu/~asdas/imo/imo/isoln/isoln733.html