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If 3^(x + y) = 81 and 81^(x - y) = 9,then what is the value of the product xy? Express your answer as a common fraction.

 Jun 26, 2022
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( 3)^(x+y) = 81 = 3^4 => x+y = 4…(1) , similarly,

(81)^(x-y) = 3 => (3)^4*(x-y)=3^1 =>4(x-y)=1

=> x - y= 1/4 [ in both cases applying the principle as the base is equal , power will be equal]

xy = {(x+y)/2}^2 -{(x-y)/2}^2

= (4/2)^2 -(1/8)^2

= 4 - 1/64 = 255/64

 Jun 26, 2022

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