Question

Tìm các số nguyên a , b , c biết:

a.( a + b + c ) = 70; b. ( a + b + c ) = -20 và c .( a + b + c ) = 50

Answer 1

\(\left\{{}\begin{matrix}a\left(a+b+c\right)=70\\b\left(a+b+c\right)=-20\\c\left(a+b+c\right)=50\end{matrix}\right.\Leftrightarrow\left(a+b+c\right)^2=100=\left(\pm10\right)^2\Rightarrow a+b+c=\pm10\) \(+,a+b+c=10\Rightarrow\left\{{}\begin{matrix}10.a=70\\10.b=-20\\10.c=50\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=7\\b=-2\\c=5\end{matrix}\right.\)

\(+,a+b+c=-10\Rightarrow\left\{{}\begin{matrix}\left(-10\right).a=70\\\left(-10\right).b=-20\\\left(-10\right).c=50\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-7\\b=2\\c=-5\end{matrix}\right.\)