Question

Find the roots of 5^(x+1) + 5^(2-x)=5^3 + 1 by factorization method.....

Answer 1

heya,,☺..

5^(x+1)+5^(2-x)=5^3+1

=)5^x*5+5^2*5^2-5^-x=126

=)5x*5+25/5^-x=126

=)let 5^x=y

then, 5y+25/y=126

=)5y^2-126y+25=0

=)5y^2-125-y+25=0

=)5y(y-25)-(y-25)=0

=)(y-25)(5y-1)=0

y=25 and y=1/5

so, 5^x=25

5^x=5^2. ( 5 is cancelled,)

x=2 or again,

y=1/5

so,5^x=5^-1

x=-1..

hence the root is 2 and -1 ..


hope it help you..
..
@rajukumar☺☺