O.VII.27
Posted: Sun Apr 19, 2009 6:31 pm
Fie \( a, b, c, d \) numere rationale nenule.
a) Aratati ca ecuatia \( (a+b\sqrt{2})x+c+d\sqrt{2}=0, x\in \mathb{R} \) are o solutie unica.
b) Daca \( x_0 \) este solutia ecuatiei date, aratati ca \( x_0\in \mathb{Q}\Leftrightarrow ad=bc \)
Probleme date la olimpiade, RMT 1/1998.
a) Aratati ca ecuatia \( (a+b\sqrt{2})x+c+d\sqrt{2}=0, x\in \mathb{R} \) are o solutie unica.
b) Daca \( x_0 \) este solutia ecuatiei date, aratati ca \( x_0\in \mathb{Q}\Leftrightarrow ad=bc \)
Probleme date la olimpiade, RMT 1/1998.