Difference between revisions of "Transylvanian Hungarian MC (Romania) 2012 - G9 - P1"
Africas1819 (talk | contribs) (Created page with "Find all numbers <math>x,y\in\mathbb N</math> for which the relation <math> x+2y+\frac{3x}{y}=2012</math> holds. Proposed by Bela Kovacs") |
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Proposed by Bela Kovacs | Proposed by Bela Kovacs | ||
+ | Solution | ||
+ | Solve for <math> x </math>. | ||
+ | <math> x=-2y+2018-\frac{6054}{y+3} </math> | ||
+ | Determine all value(s) of <math> y\in\mathbb{N} </math> | ||
+ | <math> (y+3)|6054 </math> where the positive factors of <math> 6054 </math> are <math> 1, 2, 3, 6, 2018, 3027 </math> and <math> 6054 </math>. | ||
+ | Equate each factor to <math> y+3 </math> and the values of <math> y </math> are <math> -1, 0, 3, 1006, 2015, 3024 </math> and <math> 6051 </math>, respectively. | ||
+ | Find the value of <math> x </math> when | ||
+ | <math> y= 3 </math> then <math> x= 1003 </math> | ||
+ | <math> y=1006 </math> then <math> x=0 </math> | ||
+ | <math> y= 2015 </math> then <math> x=-2015 </math> | ||
+ | <math> y= 3024 </math> then <math> x=-4032 </math> | ||
+ | <math> y= 6051 </math> then <math> x=-10085 </math> | ||
+ | |||
+ | Answer: <math> x=1003 </math> and <math> y=3 </math> |
Latest revision as of 03:18, 7 October 2016
Find all numbers for which the relation holds.
Proposed by Bela Kovacs Solution Solve for . Determine all value(s) of where the positive factors of are and . Equate each factor to and the values of are and , respectively. Find the value of when then then then then then
Answer: and