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Post Closed as "Not suitable for this site" by Benjamin L. Warren, Nemo, Friedrich Knop, Peter Mueller, Ryan Budney
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YCor
YCor
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Non-zero nessvanishing of this ternary Quadraticquadratic expression

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LSpice
LSpice
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I'm dealing with the expression $x^2+y^2+6z^2+8xy+4x+4y−6xz−6yz$. I want to show that this expression is always non-zero whenever $x,y$ and $z$ are positive integers. How does one do this? (Note that it's not always positive, e.xg. $x=1,y=20,z=9$).)

I'm dealing with the expression $x^2+y^2+6z^2+8xy+4x+4y−6xz−6yz$. I want to show that this expression is always non-zero whenever $x,y$ and $z$ are positive integers. How does one do this? (Note that it's not always positive, e.x. $x=1,y=20,z=9$).

I'm dealing with the expression $x^2+y^2+6z^2+8xy+4x+4y−6xz−6yz$. I want to show that this expression is always non-zero whenever $x,y$ and $z$ are positive integers. How does one do this? (Note that it's not always positive, e.g. $x=1,y=20,z=9$.)

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Benjamin L. Warren
Benjamin L. Warren
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Non-zero ness of this ternary Quadratic expression

I'm dealing with the expression $x^2+y^2+6z^2+8xy+4x+4y−6xz−6yz$. I want to show that this expression is always non-zero whenever $x,y$ and $z$ are positive integers. How does one do this? (Note that it's not always positive, e.x. $x=1,y=20,z=9$).