Q : (7492^4+64)(8000^4+64)(8008^4+64)/(7488^4+64)(7496^4+64)(8004^4+64) =_________


A :


a^4+64 = (a^4+16a^2+64)-(4a)^2 = (a+8)^2 - (4a)^2 = (a^2+4a+8)(a^2-4a+8) = [(a+2)^2+4][(a-2)^2+4]......(1)


(1) -->  (7490^2+4)(7494^2+4)......(8006^2+4)(8010^2+4)/(7486^2+4)(7490^4+4).....(8002^2+4)(8006^2+2)

= (8010^2+4)/(7486^2+4)

= (4010^2+1)/(3743^2+1)