2013 AMC 10B Problems/Problem 11
Revision as of 15:44, 21 February 2013 by Countingkg (talk | contribs) (Created page with "==Problem== Real numbers <math>x</math> and <math>y</math> satisfy the equation <math>x^2 + y^2 = 10x - 6y - 34</math>. What is <math>x+y</math>? <math> \textbf{(A)}\ 1 \qquad...")
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
.