Question

Se considera ecuatia x²-(2m+1)x+m+1=0, m apartine R,cu radacinile x1 si x2. Determinati m€R stiind ca x1²x2+x1x2²=0.​

Answer 1

Folosim relațiile lui Viète.

$\it x^2-(2m-1)x+m+1=0\\ \\ x_1^2x_2+x_1x_2^2=0 \Rightarrow x_1x_2(x_1+x_2)=0 \Rightarrow (m+1)(2m-1)=0 \Rightarrow \\ \\ \\ \Rightarrow \begin{cases} \it m+1=0 \Rightarrow m_1=-1\\ \\\ \it 2m-1=0 \Rightarrow m_2=0,5\end{cases}$