no value of a+B exists as such.....

2a = 169  - 121  .....................................1

2b = 11 - 13 ..................................................2

a+b = 78 - 55 .................................................3

since a and b are natural no.s(as mentioned by author of this ques)...from eqn 1

    169  121 

=>  (121/169) 

=> (1.18) .....................................4

also from eqn.2

11  13 

=>  (13/11) 

=>  (1.39) ..................................5

thus from eqn (4) and (5) no such value of a and b exists..