Question

If 2+3=43 & 3+4=109 & 7+9=1138. Now 12+16=?

Answer 1

Given :  2+3=43 3+4=109 7+9=1138

To find : 12 + 14 = ?

Solution:

2+3=43

(2 * (3 + 1) ) * (2 + 3)  +  3 ( 3 - 2)  

= 40 + 3

= 43

3+4=109

(3 * (4 + 1) ) * (3 + 4)  +  4 (4 - 3)  

= 105 + 4

= 109

7+9=1138

(7 * (9 + 1) ) * (7 + 9)  +  9 (9 - 7)  

= 1120 + 18

= 1138

12+16=

(12 * (16 + 1) ) * (12 + 16)  +  16 (16 - 12)

= 12  *17 * 28  + 16 * 4  

= 5712 + 64

= 5776

12+16  = 5776

12+14=

(12 * (14 + 1) ) * (12 + 14)  +  14 (14 - 12)

= 12  *15 * 26  + 14 * 2  

= 4680 + 28

= 4708

12+14  = 4708

Logic  

x + y = z

=> z  =   x (y+1)(x+y) +  y*(y-x)      or x²(y + 1) + y²(x + 1)   or xy(x+y) + x² + y²

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