Answer:
either x=2 or x=-2
Step-by-step 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
