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If the sum of the squares of nonnegative real numbers a,b, and c is 13, and ab + bc + ca = 6, then what is the sum of a,b, and c?

 Mar 6, 2019
 #1
avatar+103122 
+1

a^2 + b^2 + c^2  = 13

ab + bc + ca = 6

 

Just by inspection....an integer solution is  a = 0, b = 2   and c = 3

 

So

 

0^2 + 2^2 + 3^2 =   13

 

And

 

0*2 + 2*3  + 3*0   =   6

 

And their sum = 5

 

Another possible integer  solution is  (a, b, c) =   (0, 3, 2 )

 

cool cool cool

 Mar 6, 2019
edited by CPhill  Mar 6, 2019
 #2
avatar+188 
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Good anwnser Cphill. But a,b, and c are all the same, should they not be the same variable?

 Mar 6, 2019

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