The number of solutions of the trigonometric equation 1+ x 5 x= ^2 x in [0,2 ] is

Step-by-step solution

We have, array ll & 1+ x 5 x= ^2 x & 1- ^2 x+ x 5 x=0 & ^2 x+ x 5 x=0 & x( x+ 5 x)=0 & x [2 ( x+5 x 2 ) ( x-5 x 2 ) ]=0 & x(2 3 x 2 x)=0 & x=0 ; 3 x=0 or 2 x=0 & x= 2 , 3 2 or & 3 x= 2 , 3 2 , 5 2 , 7 2 , 9 2 , 11 2 or & 2 x= 2 , 3 2 , 5 2 , 7 2 & x= 2 , 3 2 , 6 , 5 6 , 7 6 , 11 6 , 4 , 3 4 , 5 4 , 7 4 array Thus, there are 10 solutions in [0,2 ]