Question

tìm a,b,c biết rằng

a(a+b+c)=36,b(a+b+c)=48,c(a+b+c)=60

Answer 1

\(\left\{{}\begin{matrix}a\left(a+b+c\right)=36\\b\left(a+b+c\right)=48\\c\left(a+b+c\right)=60\end{matrix}\right.\)

Cộng theo vế 3 pt trên ta có:

\(a\left(a+b+c\right)+b\left(a+b+c\right)+c\left(a+b+c\right)=144\)

\(\Leftrightarrow\left(a+b+c\right)^2=144\Leftrightarrow a+b+c=12\)

\(\Rightarrow\left\{{}\begin{matrix}a\cdot12=36\\b\cdot12=48\\c\cdot12=60\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a=3\\b=4\\c=5\end{matrix}\right.\)