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The non-negative real numbers x ,y and z satisfy the two equations

 

x^2 + y^2 + z^2 = 9

xy + yz + zx = 6

 

What is the sum of x, y, and z?

 Jul 30, 2022
 #1
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x^2 + y^2 + z^2 + 2(xy + yz + zx) = (x + y + z) ^2

= 21 = (x + y + z)^2

x + y + z = sqrt(21)

(Make sure you know why it's positive sqrt(21)!)

 Jul 30, 2022

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