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avatar+174 

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

 Jul 10, 2024
 #1
avatar+867 
+1

The minimum value is 5/9.

 Jul 10, 2024
 #2
avatar+20 
-1

read it as 9^x - 2(3^x) + 1, so the minimum value is 0
9^0 - 2(3^0) + 1

1 - 2(1) + 1

2 - 2

0

 Jul 11, 2024

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