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Let x > 0 and y > 0. Suppose that xy^2 = 6 and x^2*y^6 = 72xy.  What is the value of xy? Express your answer in simplest radical form. 

 Jul 12, 2022
 #1
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xy^2 = 6   →   x =  6/y^2      (1)

x^2 y^6  =  72xy      →   xy^5  =  72    (2)

 

Sub  (1)  into (2)

 

(6/y^2) * y^5  =  72

 

6 * y^3  =  72

 

y^3  =  72/6 = 12

 

y = (12)^(1/3)

 

x=  6 / [ 12^(1/3) ] ^2 =  6 / (12)^(2/3)

 

xy =  6/ (12^(2/3) * 12^(1/3)  =  6 / (12^(1/3) =    [6 ] / [ 2^(1/3) * 6^(1/3) ]   = (6)^(2/3) / (2^(1/3)  =

 

3^(2/3)  * 2^(2/3)  / 2^(1/3)  =

 

(9)^(1/3) * 2^(1/3)  = 

 

∛9 * ∛2 =

 

∛18

 

 

cool cool cool

 Jul 12, 2022

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