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.

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.x3−6x2+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.x3−9x2+17x−27=0

(x−3)3=0<=>(x−3)3=0

x−3=0<=>x−3=0

x=3