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Message: <blockquote data-quote="Persius" data-source="post: 15735011" data-attributes="member: 477838">This proof was made just now with respect to this artical  <a href="http://www.citehr.com/124991-solve-ramanujan-maths.htm" target="_blank">http://www.citehr.com/124991-solve-ramanujan-maths.htm</a> .There it is stated that this question is from RamanujanA proof for a normal mathematical problem.,very easy one,√X + Y = 7------------(1)X + √Y = 11---------(2) THIS PROBLEM DEALS WITH POSITIVE  INTEGERS I am not going to use any kind of mathematical tools like Induction here,And I wont be able to get a S pass even for the 2013 a/l maths paper. because of not having a practice about time management.I wasn't so good at time management<img src="/styles/default/xenforo/smilies/default/sad.gif"  class="smilie" loading="lazy" alt=":(" title="Sad    :(" data-shortname=":(" />ok First of all ,Lets assume that the x and  y should be  positive integers/because this is from the sector called NUMBER THEORY.IT deals only with integers/ LETS TRY TO TAKE POSITIVE VALUES <img src="/styles/default/xenforo/smilies/default/happy.gif"  class="smilie" loading="lazy" alt=":)" title="Happy    :)" data-shortname=":)" /><img src="/styles/default/xenforo/smilies/default/happy.gif"  class="smilie" loading="lazy" alt=":)" title="Happy    :)" data-shortname=":)" /><img src="/styles/default/xenforo/smilies/default/happy.gif"  class="smilie" loading="lazy" alt=":)" title="Happy    :)" data-shortname=":)" />And also both x and y are positive integers /because number theory is most oftenly about real numbers/  I mean integers //// √X=7-Y-----3  (a rearrangement) ok now lets.use simple logic here and argue it.X>0 ;so Y cannot be larger than 7 ...ok got it??2 fact-- Both X and Y are positive integers/and IF Y IS a  posiive integer ;to get the value of 7 ,another positive  integer should be added to Y ,so in here it is √X !!!!!!hmmm so it is also an integer we can argue in the other side also/If X is a positive  integer and so does the 11 .,then the value that should be added to X to get the value 11 should be also a postive  integer, and it is √Y ///hmm ok  THEN BOTH √X  & √Y  should be  postive integers....FROM 3 we get √X ,Y<7 and √Y  is also an integer then the only solution set that we  can   get that satisfy these condition is  Y = 1 or 4 ,√1=1,√4= 2so X and √X also integers If Y=1 from  (3)  √X = 6 and X = 36  but this violate the  (2) equation which is  X + √Y = 11 so//////////////// the answer is Y=4 and X=9</blockquote>

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