Question

Solve... X:5 to the power x+1 +5to the power 1-x gives 26

Answer 1

Answer:

Step-by-step explanation:

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

5 × 5^x + 5× 5^-x =26

5×5x +5 × 1/5=26

[5 ×5^x5^x+5) /5^x=26  

5 ×5^x5^x+5=26×5^x

(5×5^2x) -(26×5^x) +5=0

let 5^x = y  

(5^x) ^2= y^2

5y^2 -26y +5=0

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

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

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

y=5 , y=1/5

Now put the value of y in substitution

5^x=y or 5^x =1/5

5^x=5^1 or 5^x = 5 ^-1

x=1 or x = -1

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