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If x and y are numbers such that 9^x-4^y=10 and 3^x-2^y=2, compute $3^x+2^y$.

 May 30, 2019
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If x and y are numbers such that 9^x-4^y=10 and 3^x-2^y=2, compute $3^x+2^y$

 

We can factor   9^x - 4^y   as   (3^x - 2^y) (3^x + 2^y)  

 

So 

 

 (3^x - 2^y) (3^x + 2^y)   = 10

 

( 2) ( 3^x + 2^y)  = 10         divide both sides by 2

 

3^x + 2^y  =    5

 

 

cool cool cool

 May 30, 2019
edited by CPhill  May 30, 2019

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