Tìm x bt (phân tích đa thức thành nhân tử)
1) 2x^2-8=0
2) (x+3)^2=4
3) (x-7)^2=36
4) x^2+6x+9=0
5) x^2-14x+49=0
6) x^3-6x^2+12x-8=0
7) x^3-9x^2+27x-27=0
Tìm x bt (phân tích đa thức thành nhân tử)
1) 2x^2-8=0
2) (x+3)^2=4
3) (x-7)^2=36
4) x^2+6x+9=0
5) x^2-14x+49=0
6) x^3-6x^2+12x-8=0
7) x^3-9x^2+27x-27=0
Đáp án:
1,(2x-8)(2x+8)=0
<=>\(\left[ \begin{array}{l}2x-8=0\\2x+8=0\end{array} \right.\)
<=>\(\left[ \begin{array}{l}x=4\\x=-4\end{array} \right.\)
2,$x^{2}$+6x+9=4
$x^{2}$+6x=-5
$x^{2}$+6x+5=0
$x^{2}$+x+5x+5=0
x(x+1)+5(x+1)=0
(x+1)(x+5)=0
\(\left[ \begin{array}{l}x+1=0\\x+5=0\end{array} \right.\)
\(\left[ \begin{array}{l}x=-1\\x=-5\end{array} \right.\)
3,
,$x^{2}$-14x+49=36
$x^{2}$-14x=-13
$x^{2}$-14+13=0
$x^{2}$-x-13x+13=0
x(x-1)-13(x-1)=0
(x-1)(x-13)=0
\(\left[ \begin{array}{l}x-1=0\\x-13=0\end{array} \right.\)
\(\left[ \begin{array}{l}x=1\\x=13\end{array} \right.\)
4,
$x^{2}$+3x+3x+9=0
(x+3)(x+3)=0
\(\left[ \begin{array}{l}x+3=0\\x+3=0\end{array} \right.\)
\(\left[ \begin{array}{l}x=-3\\x=-3\end{array} \right.\)
5,
$x^{2}$-7x-7x+49=0
(x-7)(x-7)=0
\(\left[ \begin{array}{l}x-7=0\\x-7=0\end{array} \right.\)
\(\left[ \begin{array}{l}x=7\\x=7\end{array} \right.\)
6.x3−6x2+15x−8=06.×3−6×2+15x−8=0
(x−2)2=0<=>(x−2)2=0
x−2=0<=>x−2=0
x=2<=>x=2
7.x3−9x2+17x−27=07.×3−9×2+17x−27=0
(x−3)3=0<=>(x−3)3=0
x−3=0<=>x−3=0
x=3
Đáp án:
Giải thích các bước giải:
$1, 2x^2-8=0$
$(=)2(x^2-4)=0$
$(=)2(x-2)(x+2)=0$
\(\left[ \begin{array}{l}x-2=0\\x+2=0\end{array} \right.\) (=)\(\left[ \begin{array}{l}x=2\\x=-2\end{array} \right.\)
$\text{Vậy phương trình có nghiệm là $x=±2$}$
$2, (x+3)^2=4$
$(=)(x+3)^2-4=0$
$(=)(x+3-2)(x+3+2)=0$
$(=)(x+1)(x+5)=0$
\(\left[ \begin{array}{l}x+1=0\\x+5=0\end{array} \right.\) (=)\(\left[ \begin{array}{l}x=-1\\x=-5\end{array} \right.\)
$3. (x-7)^2=36$
$(=)(x-7)^2-36=0$
$(=)(x-7-6)(x-7+6)=0$
$(=)(x-13)(x-1)=0$
\(\left[ \begin{array}{l}x-13=0\\x-1=0\end{array} \right.\) (=)\(\left[ \begin{array}{l}x=13\\x=1\end{array} \right.\)
$4, x^2+6x+9=0$
$(=)(x+3)^2=0$
$(=)x+3=0$
$(=)x=-3$
$5.x^2-14x+49=0$
$(=)(x-7)^2=0$
$(=)x-7=0$
$(=)x=7$
$6.x^3-6x^2+15x-8=0$
$(=)(x-2)^2=0$
$(=)x-2=0$
$(=)x=2$
$7.x^3-9x^2+17x-27=0$
$(=)(x-3)^3=0$
$(=)x-3=0$
$(=)x=3$
Chúc bạn học tốt.