tag:blogger.com,1999:blog-6213919025256134910.post8970244408739582930..comments2023-05-15T08:32:02.241-07:00Comments on The Math Contest: 2013 - 33 &34Curmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6213919025256134910.post-83025286999180252532013-05-04T13:43:21.376-07:002013-05-04T13:43:21.376-07:00Yup, that makes sense. Yup, that makes sense. Curmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-6213919025256134910.post-41230320669174374462013-05-04T13:10:58.082-07:002013-05-04T13:10:58.082-07:00Both great questions: For #34 consider breaking th...Both great questions: <br>For #34 consider breaking the equation into the four possible intervals:<br><br>When x+y>=0 and x-y>=0 (or y>=-x and y<=x) we have: x+y+x-y=10. x=5 and -5<=y=<5<br><br>When x+y>=0 and x-y<=0 (or x>=-y and x<=y) we have: x+y-x+y=10. y=5 and -5<=x=<5<br><br>When x+y<=0 and x-y>=0 (or x<=-y and x>=y) we have: -x-y+x-y=10. y=-5 and -5<=x=<5<br><br>When x+y<=0 and x-y<=0 (or y<=-x and y>=x) we have: -x-y-x+y=10. x=-5 and -5<=y=<5<br><br>The expression implies we want the largest value of |x| and largest value of –y. We should pick x=+-5 and y=-5. This gives us 25+25+40 or 90.<br><br><br>Anonymousnoreply@blogger.com