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Find the minimum value of (x+1x)6(x6+1x6)2(x+1x)3+(x3+1x3) for x > 0. 

 Jun 9, 2019
 #1
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The expression has a minimum value of 6, when x = 1.

 Jun 9, 2019
 #2
avatar+118711 
+2

(x+1x)6(x6+1x6)2(x+1x)3+(x3+1x3)

 

Just by inspection I can see that as x moves away from 1 in either direction the function value will increase.

So the minimum will occur when x=1

that minimum will be

 

262223+2=6010=6

 

Just as our guest said,

 Jun 10, 2019

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