We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
93
1
avatar

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

 May 4, 2019
 #1
avatar+102947 
+2

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

27 Online Users

avatar
avatar