2013 AMC 10B Problems/Problem 11
Revision as of 16:47, 21 February 2013 by Richard4912 (talk | contribs) (moved 2013 AMC 10B Problems/Problem 10 to 2013 AMC 10B Problems/Problem 11: The content of this page is actually problem 11)
Problem
Real numbers and
satisfy the equation
. What is
?
Solution
If we complete the square after bringing the x and y terms to the other side, we get . Squares of real numbers are nonnegative, so we need both
and
to be
. This obviously only happens when
and
.