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Prove that it is never zero.?
Prove that x² + y² + xy ≠ 0 where x and y are integers
Yes I regret ! Additional condition is x ≠ 0 and y ≠ 0.
3 Answers
- L. E. GantLv 78 years agoFavorite Answer
0 is an integer, so x=y=0 satisfies the equation
....
Otherwise, if x^2 + y^2 +xy = 0
x = y(-1 +/- i√3)/2
in which case x can be an integer
only if y = 1/(-1 + i√3) or y = 1/(-1 - i√3), which can't be an integer which contradicts the assumption that x and y are integers.
- Anonymous8 years ago
But zero is an integer, and if x=y=0, then the expression DOES equal 0. You must have left out some conditions on x and y.
- fizixxLv 78 years ago
x² + y² = c - xy, where "c" is just some constant.
Since x² + y² is strictly positive and if c = 0 you would have the contradiction that x² + y² = -xy, which is not possible.
