^ If =1+ _ r=1 ^6(-3)^ r-1 ¹² C _ 2 r-1 , then the distance of the point (12, 3 ) from the line x- 3 y+1=0 is _________.

Step-by-step solution

aligned & =1+ _ r =1 ^6(-1)^ r -1 ¹² C _ 2 r -1 3^ r -1 & =1+ _ r =1 ^6 ¹² C _ 2 r -1 ( 3 i )^ 2 t -1 3 i i = iota, let 3 i = x aligned aligned & =1+ 1 3 i ( ¹² C ₁ x + ¹² C ₃ x ^3+ . ¹² C ₁₁ x ¹¹ ) & =1+ 1 3 i ( (1+ 3 i )¹²-(1- 3 i )¹² 2 ) aligned =1+ 1 3 i ( (-2 w ^2 )¹²-(2 w )¹² 2 )=1 so distance of (12, 3 ) from x- 3 y+1=0 is 12-3+1 2 =5