Question

solution of this eqn 2^x-x-1=0

Answer 1

take $2^x-x-1=0 \\ 2^x=x+1$
put x=1
2=2 hence 1 is root of the equation
then put
x=0
1=1
hence 1 is also a root
so x=1,0

Answer 2

put x=0 in the above equation then 2^0-0-1=0
1-0-1=0
0=0
now put x=1 in the above equation then 2^1-1-1=0
2-1-1=0
2-2=0
0=0
put x=2
2^2-2-1=0
4-2-1=0
2-1=0
1!=0
hence 0 and 1 are roots for the given equation