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`        FIND ALL PAIRS  {x,y}of integers such thatxy+   x3+y3/3= 2007`
2 years ago

NIKHIL
22 Points
```							rewrite the equation as  x3+y3-1+3xy= 6020factoring both sides we get (x+y-1)(x2+y2+1+x+y-xy) 22.5..7.43since x2+y2+1+x+y-xy= (x+y-1)2+3x+3y-3xy. now taking the above equality mode 3, we deduce thatx+y-1=2(mod 3)also x+y-1 is less than x2+y2+1+x+y-xy.so the possible values for x+y-1 are 2,5,14,20 and 35now finally by inspection we obtained that  x+y-1=20 and finally {x,y} = {18,3}or {3,18}
```
2 years ago
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• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions