BITSAT Mathematics Question (2024) — Solution

Step-by-step solution

aligned & Given, 9 = \\ & 9 - =0 \\ & 2 ( 9 + 2 ) ( 9 - 2 )=0 \\ & [ C- D=2 ( C+D 2 ) ( C-D 2 ) ] \\ & 2 5 4 =0 \\ & Either 5 =0 or 4 =0 , also [0,2 ] \\ & 5 =(2 n+1) 2 \\ & or 4 =n \\ & =(2 n+1) 10 or = n 4 \\ & = 10 , 3 10 , 2 , 7 10 , 9 10 , 11 10 , 13 10 , 3 2 , 17 10 , 19 10 \\ & or 0, 4 , 2 , 3 4 , , 5 4 , 3 2 , 7 4 , 2 \\ & Total number of solutions =17 \\ & ( 2 and 3 2 are common ) aligned