Question

Cho PT: x²-2(m+2)x + m²+7=0 Tìm m để pt cõ 2 nghiệm x1;x2 thoả mãn x1.x2-2(x1+x2)= 4 (Giúp mk vs ạ )

Answer 1

\(\Delta'=\left(m+2\right)^2-m^2-7=4m-3\ge0\Rightarrow m\ge\frac{3}{4}\)

Khi đó theo Viet, pt có 2 nghiệm thỏa: \(\left\{{}\begin{matrix}x_1+x_2=2\left(m+2\right)\\x_1x_2=m^2+7\end{matrix}\right.\)

\(x_1x_2-2\left(x_1+x_2\right)=4\)

\(\Leftrightarrow m^2+7-4\left(m+2\right)-4=0\)

\(\Leftrightarrow m^2-4m-5=0\)

\(\Rightarrow\left[{}\begin{matrix}m=5\\m=-1< \frac{3}{4}\left(l\right)\end{matrix}\right.\)