NMOS 2010 Q15

Q15. a, b, c and d are letters that represent four different positive integers such that axa+bxb=cxc+dxd. Find the least possible value of axa+bxb.


a x a + b x b = c x c + d x d


a x a – c x c = d x d – b x b


(a + c) x (a - c) = (d + b) x (d - b)


(8 + 7) x (8 - 7) = (4 + 1) x (4 - 1)



8 x 8 + 1 x 1 = 7 x 7 + 4 x 4 = 65