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Find the minimum value of \(9^x - 3^x + 1\) over all real numbers x.

 May 4, 2019
 #1
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Let  3^x  = m      .....so........(3^x)^2  = (3^2)^x   = m^2  = (9)^x

 

So we have

 

m^2 - m + 1    complete the square on m

 

m^2 - m + 1/4 + 1 - 1/4

 

(m - 1/2)^2 + 3/4

 

And this will be a minimum  of 3/4   when  m = 1/2

 

 

cool cool cool

 May 4, 2019

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