Question

对于非零自然数m和n,规定符△的含义：m△n=am+n/2mn,a为一个确定的整数3△6=4△5,那么4△6=?

Answer 1

3△6

= (A*3+6)/(2*3*6) = (A+2)/12

4△5

= (A*4+5)/(2*4*5) = (4A+5)/40

则有方程

(A+2)/12 = (4A+5)/40

解得A = 2.5

4△6

= (2.5*4 + 6)/ (2*4*6)

= 16/48

= 1/3