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Find the minimum value of 9^x - 2 \cdot 3^x + 1 over all real numbers x.

 Aug 17, 2024
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\(9^{x}-2\cdot 3^{x}+1\):

 

Set a = \(3^x\)

 

\(a^2-2a+1=0\)

\((a-1)^2=0 \)

a=1, so \(3^x\)=1

 

That means x=0 because anything to the 0th power is one

 

Hope this helps! 

 

 ðŸ¤™ ðŸ¤™ ðŸ¤™

 Aug 17, 2024

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