If a³ = 117 + b³ and a = 3 + b, then the value of a + b is?

Solution (By Examveda Team)

$$\eqalign{ & {a^3} = 117 + {b^3}{\text{ , }}a = 3 + b \cr & {a^3} - {b^3}{\text{ = 117}}\,......{\text{(i)}} \cr & a - b = 3\,........(ii) \cr & {\text{Put }}a = 5,{\text{ }}b = 2 \cr & {\text{Both equation satisfy}} \cr & {\text{Now, }}a + b = 5 + 2 = 7 \cr} $$