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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 + xz + yz = 18

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

 Feb 1, 2022
 #1
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Use the following algebraic identity:

(x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + xz + yz) = 9 + 2(18) = 45

 Feb 1, 2022

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