Positive, non-negative or negative

Algebra Level pending

Numbers x , y , z x, y, z are real and positive. What can be said about ( x y + y z + z x ) 3 − 27 x 2 y 2 z 2 (xy +yz +zx) ^3-27x^2y^2z^2 ?

Nothing can be said Always non-negative Always negative Always positive

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Nitin Kumar
May 8, 2020

Apply AM-GM on xy, yz and zx. The result is immediate.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Cantdo Math
Apr 18, 2020

Apply am-gm of three variables.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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