Guest Posted March 17, 2010 Report Share Posted March 17, 2010 (edited) Determine all possible quadruplet(s) (A, B, C, D) of positive integers, with A >= C, that satisfy this system of equations: A*B = C + 2*D, and: C*D = A + 2*B Prove that no other quadruplet(s) satisfy the above system of equations. Edited March 17, 2010 by K Sengupta Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 18, 2010 Report Share Posted March 18, 2010 Let a = nc Let b = md Then; mncd = c + 2d cd = nc + 2md Combining both equaitons, mn²c + 2m²nd = c + 2d This means that both m and n must be 1 so, a = c and b = d This gives the equation as cd = c + 2d let c = xd Then, xd² = d(x+2) x(d-1) = 2 This is possible when x = 1 or x = 2 Then, d = 3 and d = 2 respectively Accordingly, the quadruplets (a,b,c,d) are, (4,2,4,2) and (3,3,3,3) Quote Link to comment Share on other sites More sharing options...
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Determine all possible quadruplet(s) (A, B, C, D) of positive integers, with A >= C, that satisfy this system of equations:
A*B = C + 2*D, and:
C*D = A + 2*B
Prove that no other quadruplet(s) satisfy the above system of equations.
Edited by K SenguptaLink to comment
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