Suppose we have the follwing two identities:
(Ax-26)(Bx^2+Cx+D)=8x^3-2197
and (Ex-52)(Fx^2+Gx+H)=8x^3-2197;

Compute the quantity ((13B/2 + 2D/13 + AB)+(13F/2+2H/13+EF)).

(In reply to No Subject by Jun)

By multiplying out the various polynomials using your results for A-H, I confirm that your results for A-H are correct. However, my calculational skills (today, at least) appear to be suspect, so this should not be considered definitive!  Nevertheless, using your results, I am going to take a stab at computing the quantity  ((13B/2 + 2D/13 + AB)+(13F/2+2H/13+EF)):

13*2/2 + 2*84.5/13 + 4*2 = 13 + 13 + 8 = 34

13*1/2 + 2*42.25/13 + 8*1 = 6.5 + 6.5 + 8 = 21

34 + 21 = 55

I hope I did this one correctly.  The significance of this quantity escapes me completely, though.

Posted by Richard on 2005-02-11 19:18:00