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# Help algebra

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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 2, 2021

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Notice that $$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zx$$. You could multiply the second equation by 2 and then add the equations up:

$$x^2+y^2+z^2+2xy+2yz+2zx=9+6\cdot2\\(x+y+z)^2=21$$

Take the square root of both sides and you will arrive at the answer.

(notice that the negative square root is extraneous since x, y, and z are all nonnegative)

Jul 2, 2021