Number of solutions of equations 9 = in the interval [0,2 ] is

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