If the sum of the roots of the equation 4 x+6=7 2 x in the interval [0,314] is k , k R . Find k .

Step-by-step solution

aligned & 4 x+6=7 2 x & 2 ^2 2 x-1+6=7 2 x & 2 ^2 2 x-7 2 x+5=0 & 2 ^2 2 x-2 2 x-5 2 x+5=0 & 2 2 x( 2 x-1)-5( 2 x-1)=0 & ( 2 x-1)(2 2 x-5)=0 aligned aligned & 2 x= 5 2 ( not possible ) & 2 x=1 aligned aligned & 2 x=2 n & x=n aligned sum in [0,314] is [1+2+3+ +100]-100 =5050 -100 =4950 k=4950