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
86
2
avatar+480 

Answer: 48sqrt(6)

 Mar 16, 2019
 #1
avatar+101086 
+1

y =    8x^3  + 36x  + 54x^(-1) + 27x^(-3)        take the derivative....set to 0

 

y '  =  24x^2 + 36 - 54x^(-2) - 81x^(-4)  = 0   

 

y ' = 3 ( 8x + 12 - 18x^(-2) - 27x^(-4)  )  =  0

 

8x^2 + 12 - 18x^(-2) - 27x^(-4) = 0

 

8x^6 + 12x^4 - 18x^2 - 27 = 0   factor

 

4x^4 ( 2x^2 + 3)  -  9(2x^2 + 3)  = 0

 

(4x^4 - 9) (2x^2 + 3) = 0      the second factor gives a non-real answer when set to 0

 

So

 

4x^4 - 9 = 0

4x^4 = 9

x^4 = 9/4

x =  (9/4)^(1/4)  =  [(3/2)^2] ^(1/4)  = √[3/2]

 

Subbing this back into the original function

 

8[√[3/2] ]^3 + 36(√[3/2] ) + 54 / (√[3/2]) + 27 / [ √[3/2] ]^3   =

 

8 (3/2)(√[3/2] )  + 18√6   +     54 ( √[ 3/2] ) / (3/2)   +  27 /  [ (3/2) √[3/2] )

 

12√[3/2]   + 18√6 +  + 36  √[3/2]  +   18 / √[3/2]

 

6√6  + 18√6  + 18√6   +  6√6  =

 

48√6

 

 

cool  cool cool

 Mar 16, 2019
 #2
avatar+480 
0

Thanks!!!

dgfgrafgdfge111  Mar 18, 2019

7 Online Users