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5^x+1 + 5^1-x=26 Find x

5^x+1 + 5^1-x=26
Find x

Grade:9

3 Answers

sanatan sharma
26 Points
9 years ago

5^x+1 + 5^1-x=26

(5)(5x) + (5)/(5x) = 26

5(5x + 1/(5x))=26

considering 5x = y the equation becomes 

5y2 - 26y +5 = 0

or

y = 5 , 1/5

therefore x = 1 , -1


G Narayana Raju
51 Points
9 years ago

5x+1 + 51-x=26

(5)(5x) + (5)/(5x) = 26

5(5x + 1/(5x))=26

let m=5x

5m2 - 26m +5 = 0

5m2-25m-m+5=0

5m(m-5)-(m-5)=0

(5m-1)(m-5)=0

m= 5 , 1/5

thus x = 1 , -1.

Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the solution to your problem.
 
5x+1 + 51-x=26
(5)(5x) + (5)/(5x) = 26
5(5x + 1/(5x))=26
let m=5x
Hence, 5m2 - 26m +5 = 0
5m2-25m-m+5=0
5m(m-5)-(m-5)=0
(5m-1)(m-5)=0
m= 5 , 1/5
thus 5x = 5  or  5x = 1/5
Hence, x = 1 or – 1
 
Thanks and regards,
Kushagra

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