Question

Solve:
5^x+1/5^x=25 1/25​

Answer 1

either x=2 or x=-2

Explanation:

let 5^x be a then,

a+1/a=626/25

or,25(a^2+1)=626a

or,25a^2+25-626a=0

or,25a^2-626a+25=0

or,25a^2-(625+1)a+25=0

or,25a^2-625a-a+25=0

or,25a(a-25)-1(a-25)=0

or,(a-25)(25a-1)=0

either,

a-25=0

or,a=25

or,5^x=5^2

equating the powers we get,

x=2

or,

25a-1=0

or,a=1/25

or,5^x=1/5^2

or,5^x=5^-2

equating the powers we get,

x=-2

Answer 2

x = -2 I think that the right answer