Difference between revisions of "Mock AIME 3 2006-2007 Problems/Problem 11"
(Created page with "Factoring the LHS gives <math>2x(x+y)=6+x^2+y^2</math>. Now converting to polar: <math>2r\cos(a)(r\cos(a)+r\sin(a))=6+r^2</math> <math>2\cos(a)(\cos(a)+\sin(a))=\frac{6}{r^2}+1...") |
(No difference)
|
Revision as of 20:27, 15 February 2015
Factoring the LHS gives .
Now converting to polar:
Since we want to find ,
Since we want the minimum of this expression, we need to maximize the denominator. The maximum of the sine function is 1
(one value of which produces this maximum is )
So the desired minimum is