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MathTime • Vezi subiect - Tabăra MathTime - Problema 2, Ziua I - JUNIORI

Tabăra MathTime - Problema 2, Ziua I - JUNIORI

Tabăra MathTime - Problema 2, Ziua I - JUNIORI

Mesajde Laurențiu Ploscaru » Lun Sep 05, 2011 8:46 am

Rezolvați în \Bbb{Z} ecuația (xy-7)^2=x^2+y^2.
People are strange when you're a stranger,
Faces look ugly when you're alone.
Women seem wicked when you're unwanted,
Streets are uneven when you're down.
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Re: Tabăra MathTime - Problema 2, Ziua I - JUNIORI

Mesajde andreiteodor » Lun Sep 05, 2011 2:38 pm

Ecuatia data este echivalenta cu :
[unparseable or potentially dangerous latex formula].
Cum primul factor este mai mic decat al doilea, se disting doua cazuri. Rezolvand sistemele rezultate, obtinem solutiile :
(3;4);(4;3);(0;7);(7;0).
Nimic nu-i niciodata asa de simplu cum pare.
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Re: Tabăra MathTime - Problema 2, Ziua I - JUNIORI

Mesajde ghenghea1 » Vin Dec 26, 2014 1:54 pm

Putem sa notam s=x+y si p=xy
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Re: Tabăra MathTime - Problema 2, Ziua I - JUNIORI

Mesajde ghenghea1 » Mie Ian 07, 2015 10:35 pm

Putem scrie ecuatia astfel (xy-6)^2 + 13=(x+y)^2 <=>(xy-6-x-y)(xy-6+x+y)=-13...
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