Tìm x biết :a, x^2-x-6 b, (x-2).(x^2+2x+7)+2.(x^2-4)-5.(x-2)=0 11/07/2021 Bởi Ivy Tìm x biết :a, x^2-x-6 b, (x-2).(x^2+2x+7)+2.(x^2-4)-5.(x-2)=0
Đáp án: a) $\left[\begin{array}{l} x =3\\x =-2\end{array}\right.$ b) $x = 2$ Giải thích các bước giải: $\begin{array}{l}a)\,\,x^2 – x – 6 = 0\\ \Leftrightarrow x^2 – 3x + 2x – 6 = 0\\ \Leftrightarrow x(x-3) + 2(x-3) = 0\\ \Leftrightarrow (x-3)(x+2) = 0\\ \Leftrightarrow \left[\begin{array}{l} x – 3 = 0\\x + 2 =0\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l} x =3\\x =-2\end{array}\right.\\ b)\,\,(x-2)(x^2 + 2x + 7) + 2(x^2 -4)- 5(x-2)=0\\ \Leftrightarrow (x-2)(x^2 + 2x + 7 + 2(x+2) – 5) = 0\\ \Leftrightarrow (x-2)(x^2 +4x +6) = 0\\ \Leftrightarrow \left[\begin{array}{l}x – 2 = 0\\x^2 + 4x + 6 = 0 \quad (vô\,\,nghiệm)\end{array}\right.\\ \Leftrightarrow x = 2 \end{array}$ Bình luận
Đáp án:
a) $\left[\begin{array}{l} x =3\\x =-2\end{array}\right.$
b) $x = 2$
Giải thích các bước giải:
$\begin{array}{l}a)\,\,x^2 – x – 6 = 0\\ \Leftrightarrow x^2 – 3x + 2x – 6 = 0\\ \Leftrightarrow x(x-3) + 2(x-3) = 0\\ \Leftrightarrow (x-3)(x+2) = 0\\ \Leftrightarrow \left[\begin{array}{l} x – 3 = 0\\x + 2 =0\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l} x =3\\x =-2\end{array}\right.\\ b)\,\,(x-2)(x^2 + 2x + 7) + 2(x^2 -4)- 5(x-2)=0\\ \Leftrightarrow (x-2)(x^2 + 2x + 7 + 2(x+2) – 5) = 0\\ \Leftrightarrow (x-2)(x^2 +4x +6) = 0\\ \Leftrightarrow \left[\begin{array}{l}x – 2 = 0\\x^2 + 4x + 6 = 0 \quad (vô\,\,nghiệm)\end{array}\right.\\ \Leftrightarrow x = 2 \end{array}$