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Find the minimum value of

Y=x^2+1/x

For x>0

 

 

Also,

If x,y, and z are positive integers such that x^2+y^2+z^2=174. What is the greatest value of x+y+z?

 Dec 15, 2018
 #1
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Find the minimum value of

Y=x^2+1/x

 

Take the derivative  and set to    0

 

y '  = 2x  - 1/x^2  =  0

 

So

 

2x -  1/x^2   = 0

2x = 1/x^2

2x^3 = 1

x^3  =  1/2

x =  ∛(1/2)      ⇒   this is the x value that minimizes the function

 

The minimum value is

 

[ (1/2)^(1/3) ] ^2   +   1 / (1/2)^(1/3)  =

 

(1/2)^(2/3)  + 1 / (1/2)^(1/3)  ≈  1.89

 

 

 

If x,y, and z are positive integers such that x^2+y^2+z^2=174. What is the greatest value of x+y+z?

 

The greatest value  of x + y + z  is when we have the  triplet  5, 7, 10

 

And the sum  =  22

 

 

cool cool cool

 Dec 15, 2018

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