Question

\(\left\{{}\begin{matrix}u_1+u_2+u_3=-12\\u_1u_2u_3=80\end{matrix}\right.\)

tìm u₁ và công sai d

Answer 1

\(\Rightarrow\left\{{}\begin{matrix}u_1+\left(u_1+d\right)+\left(u_1+2d\right)=-12\\u_1\left(u_1+d\right)\left(u_1+2d\right)=80\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}u_1+d=-4\\u_1.\left(-4\right).\left(u_1+2d\right)=80\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}u_1=-4-d\\u_1\left(u_1+2d\right)=-20\end{matrix}\right.\)

\(\Rightarrow\left(-4-d\right)\left(-4-d+2d\right)=-20\)

\(\Rightarrow\left(d+4\right)\left(d-4\right)=20\)

\(\Rightarrow d^2-16=20\Rightarrow d=\pm6\)

- Với \(d=6\Rightarrow u_1=-10\)

- Với \(d=-6\Rightarrow u_1=2\)