OJM 2014, problema 1
-
Laurențiu Ploscaru
- Mesaje: 1237
- Membru din: Mie Mai 04, 2011 5:42 pm
- Localitate: Călimănești
- Contact:
OJM 2014, problema 1
Să se rezolve în mulţimea numerelor complexe ecuaţia: $|z-|z+1||=|z+|z-1||$.
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.
Faces look ugly when you're alone.
Women seem wicked when you're unwanted,
Streets are uneven when you're down.
-
Marius Stănean
- Mesaje: 751
- Membru din: Mar Iul 13, 2010 7:15 am
- Localitate: Zalau
Re: OJM 2014, problema 1
Prin ridicare la patrat ecuatia este echivalenta cu
$(z-|z+1|)(\overline z-|z+1|)=(z+|z-1|)(\overline z+|z-1|)\Longleftrightarrow$
$(z+\overline z)(|z+1|+|z-1|-2)=0\Longrightarrow z=\beta i,\beta\in\Bbb{R} \mbox { sau } z\in[-1,1]$
$(z-|z+1|)(\overline z-|z+1|)=(z+|z-1|)(\overline z+|z-1|)\Longleftrightarrow$
$(z+\overline z)(|z+1|+|z-1|-2)=0\Longrightarrow z=\beta i,\beta\in\Bbb{R} \mbox { sau } z\in[-1,1]$
Quae nocent docent