x^2+ y^2+ z^2 − xy − yz − zx = 3
#solve for all triples(x,y,z) for positive integers
fading steppe
severe ice
(x-y)^2 + (x-z)^2 + (y-z)^2 = 6
then you can simply find the integer values that solve this
a=x-y
b=x-z
c=y-z
a^2 + b^2 + c^2 = 6
severe ice
so if you multiply both sides by 2 then you can factorise it down to those terms
fading steppe
could u do it and make a full explanation
severe ice
so:
2x^2 + 2y^2 + 2z^2 - 2xy - 2yz - 2zx = 6
which then if you group terms you can complete the square:
2x^2 - 2xy - 2xz + 2y^2 - 2yz + 2z^2
(x-y)^2 + (x-z)^2 + (y-z)^2 = 6
fading steppe
can you do a full explanation with the full answer with like a mathematical bot that writes the formulas
severe ice
if you dont know how to complete the square of that form then i suggest you look into converting an implicit formula into a circle formula
fading steppe
could u just maybe continue and give the full explanation
severe ice
could u just maybe continue and give the full explanation
no