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If √x -√y+√z=0, which of the following is true? A. x^

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by Max@Math Revolution » Mon Mar 28, 2016 9:43 pm
If √x -√y+√z=0, which of the following is true?

A. x^2+y^2+z^2=xy+xz+yz
B. x^2+y^2+z^2=2xy+2xz+2yz
C. x^2+y^2-z^2=2xy+2xz-2yz
D. x^2-y^2-z^2=xy+xz+yz
E. x^4+y^4+z^4=2xy+2xz+2yz


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by regor60 » Tue Mar 29, 2016 10:29 am
Test answer choices. Use x=4, y=9,z=1 since they satisfy the equation.

Answer choice A doesn't work, Answer choice B does, choices C-E don't work

Choose B
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by Max@Math Revolution » Wed Mar 30, 2016 10:22 pm
If √x -√y+√z=0, which of the following is true?

A. x^2+y^2+z^2=xy+xz+yz
B. x^2+y^2+z^2=2xy+2xz+2yz
C. x^2+y^2-z^2=2xy+2xz-2yz
D. x^2-y^2-z^2=xy+xz+yz
E. x^4+y^4+z^4=2xy+2xz+2yz


If you square the both equations, they become x+z+2√xz=y, x+z-y=-2√xz. If you once again square the both equations, x^2+z^2+y^2+2zx-2xy-2zy=4xz is derived and eventually becomes x^2+y^2+z^2=2xy+2yz+2zx.
Thus, the answer is B.
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