If _ r=1 ¹³ 1 ( 4 +(r-1) 6 ) ( 4 + r 6 ) =a 3 +b, a, b Z , then a^2+b^2 is equal to :

Step-by-step solution

1 6 _ r=1 ¹³ [ ( 4 + r 6 )- ( 4 )-(r-1) 6 ] ( 4 +(r-1) 6 ) ( 4 + r 6 ) aligned & 1 6 _ r =1 ¹³ ( ( 4 +( r -1) 6 )- ( 4 + r 6 ) ) & =2 3 -2= 3 + b aligned So a^2+b^2=8