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Solve : 5(5^x+5^-x)=26

Solve:
5(5^x+5^-x)=26

Grade:9

4 Answers

Vijay Mukati
askIITians Faculty 2590 Points
8 years ago
Dear Student. Assume 5x= y and then try to solve the quadratic equation in terms of y. Then replace back the orginial value of y and find the value of x. Thanks.
Abishek arun
153 Points
8 years ago
5(5x + 5-x) = 26
let 5x  = y so 5-x = 1/y
5(y + 1/y) = 26
5( (y2 + 1)/y ) = 26
(y2 + 1)/y = 26/5
so 5x = 5 
x = 1
Chandrabhushan Reddy Chigarapalli
25 Points
7 years ago
Assume 5x=y. Then 5-x becomes 1/y. By simplyfying you will get a quadratic in variable y. Solve and find the value of y by using quadratic formula. After getting the value of y by using the law i.e., if bases are equal then powers should be eqauted. Finally you will get the value of x.
 
                 PLEASE APPROVE IF I AM CORRECT
Rohan Raman Arora
24 Points
7 years ago
Let 5^x = t
 
Therefore, 5(t + 1/t) = 26
=> 5(t^2 + 1) = 26t
=> 5t^2 – 26t + 5 = 0
=> (5t-1)(t-5) = 0
t = 1/5, 5
5^x = 1/5, 5
 
Therefore, 
x = -1, 1

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