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x + 1 = ( x + 1 )2
x + 1 = x2 + 2x + 1
x - 2x - x2 = - 1 + 1
- x - x2 = 0
- x ( x + 1) = 0
TH1: - x = 0 suy ra x = 0
TH2: x + 1 = 0 suy ra x = - 1
Vậy x = 0 hoặc x = - 1.

\(2x^2+5x-3=0\)
\(\Leftrightarrow2x^2-x+6x-3=0\)
\(\Leftrightarrow x\left(2x-1\right)+3\left(2x-1\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x+3=0\\2x-1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=\frac{1}{2}\end{cases}}}\)

\(\Rightarrow\left(x^2-4x+4\right)-\left(x^2-9\right)-6=0\)
\(\Rightarrow x^2-4x+4-x^2+9-6=0\)
\(\Rightarrow-4x=-7\Rightarrow x=\frac{7}{4}\)
bạn Nguyễn Gia Triệu ơi :
Cho mik hỏi là làm sao bạn ra được -7 vậy

a: Xét ΔABC có
AM là đường trung tuyến
G là trọng tâm
Do đó: \(\dfrac{AG}{AM}=\dfrac{2}{3}\)
Xét ΔABM có DG//BM
nên \(\dfrac{AD}{AB}=\dfrac{AG}{AM}\)
=>\(\dfrac{AD}{AB}=\dfrac{2}{3}\)
b: Xét ΔAMC có GE//MC
nên \(\dfrac{AE}{AC}=\dfrac{AG}{AM}\)
=>\(\dfrac{AE}{AC}=\dfrac{2}{3}\)
=>\(AE=\dfrac{2}{3}AC\)
AE+EC=AC
=>\(EC+\dfrac{2}{3}AC=AC\)
=>\(EC=\dfrac{1}{3}AC\)
\(AE=\dfrac{2}{3}AC=2\cdot\dfrac{1}{3}\cdot AC=2\cdot EC\)


Câu 5:
a. $|x+\frac{4}{5}|-\frac{1}{7}=0$
$|x+\frac{4}{5}|=\frac{1}{7}$
$\Rightarrow x+\frac{4}{5}=\pm \frac{1}{7}$
$\Rightarrow x=\frac{-23}{35}$ hoặc $x=\frac{-33}{35}$
v.
$2x+5-(x-7)=18$
$2x+5-x+7=18$
$x+12=18$
$x=6$
c.
$2(x+1)+4^2=2^4$
$2(x+1)+16=16$
$2(x+1)=0$
$x+1=0$
$x=-1$
d.
$\frac{x-3}{x+5}=\frac{5}{7}$
$\Rightarrow 7(x-3)=5(x+5)$
$\Rightarrow 7x-21=5x+25$
$\Rightarrow 2x=46$
$\Rightarrow x=23$
Câu 5:
\(a,\left|x+\dfrac{4}{5}\right|-\dfrac{1}{7}=0\\ \Leftrightarrow\left|x+\dfrac{4}{5}\right|=\dfrac{1}{7}\\ \Leftrightarrow\left[{}\begin{matrix}x+\dfrac{4}{5}=\dfrac{1}{7}\\x+\dfrac{4}{5}=-\dfrac{1}{7}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}-\dfrac{4}{5}\\x=-\dfrac{1}{7}-\dfrac{4}{5}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{23}{35}\\x=-\dfrac{33}{35}\end{matrix}\right.\\ b,2x+5-\left(x-7\right)=18\\ \Leftrightarrow2x-x=18-5-7\\ \Leftrightarrow x=6\\ c,2\left(x+1\right)+4^2=2^4\\ \Leftrightarrow2\left(x+1\right)=2^4-4^2=16-16\\ \Leftrightarrow2\left(x+1\right)=0\\ \Rightarrow x+1=0\\ \Leftrightarrow x=0-1=-1\\ d,\dfrac{x-3}{x+5}=\dfrac{5}{7}\left(x\ne-5\right)\\ \Leftrightarrow7\left(x-3\right)=5\left(x+5\right)\\ \Leftrightarrow7x-21=5x+25\\ \Leftrightarrow7x-5x=25+21\\ \Leftrightarrow2x=46\\ \Leftrightarrow x=23\)


1. (A+B)2 = A2+2AB+B2
2. (A – B)2= A2 – 2AB+ B2
3. A2 – B2= (A-B)(A+B)
4. (A+B)3= A3+3A2B +3AB2+B3
5. (A – B)3 = A3- 3A2B+ 3AB2- B3
6. A3 + B3= (A+B)(A2- AB +B2)
7. A3- B3= (A- B)(A2+ AB+ B2)
8. (A+B+C)2= A2+ B2+C2+2 AB+ 2AC+ 2BC
* CHÚ Ý;
a/ a+b= -(-a-b) ; b/ (a+b)2= (-a-b)2 ; c/ (a-b)2= (b-a)2 ; d/ (a+b)3= -(-a-b)3 e/ (a-b)3=-(-a+b)3
(a+b)^2=a^2+2ab+b^2
(a-b)^2=a^2-2ab+b^2
a^2-b^2=(a+b)(a-b)
(a+b)^3=a^3+3a^2b+3ab^2+b^3
(a-b)^3=a^3-3a^2b+3ab^2-b^3
a^3+b^3=(a+b)(a^2-ab+b^2)
a^3-b^3=(a-b)(a^2+ab+b^2)
a) \(x^2-3x=0\)
\(\Leftrightarrow x\left(x-3\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=3\end{cases}}\)
b) \(x^5-9x=0\)
\(\Leftrightarrow x\left(x^4-9\right)=0\)
\(\Leftrightarrow x\left(x^2-3\right)\left(x^2+3\right)=0\Leftrightarrow x\in\left\{0;\pm\sqrt{3}\right\}\)
c) \(PT\Leftrightarrow x^2\left(x-4\right)-\left(x-4\right)=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x-4\right)=0\Leftrightarrow x\in\left\{4;\mp1\right\}\)
d) \(PT\Leftrightarrow\left(2x+5\right)^2\left(2x-5\right)^2-9\left(2x-5\right)^2=0\)
\(\Leftrightarrow\left(2x-5\right)^2\left[\left(2x+5\right)^2-9\right]=0\)
\(\Leftrightarrow\left(2x-5\right)^2\left(2x+2\right)\left(2x+8\right)=0\Leftrightarrow x\in\left\{\frac{5}{2};-1;-4\right\}\)