Câu hỏi của Đặng Thị Thùy Phương

Question

1/ Rút gọn các biểu thức sau :

a) ( x + y )²- ( x - y )² ; b) ( a + b )³ + ( a - b)³ - 2a³ ; c...

Trịnh Công Mạnh Đồng · Accepted Answer

4.a) $2x^2-10x-3x-2x^2-26=0$

$-13x-26=0\Rightarrow-13\left(x+2\right)=0$

$\Rightarrow x=-2$

b) $2\left(x+5\right)-x^2-5x=0$

$2x+10-x^2-5x=0\Leftrightarrow-x^2-3x+10=0$

$-\left(x^2+3x-10\right)=0$

$-\left(x^2-2x+5x-10\right)=-\left(x\left(x-2\right)+5\left(x-2\right)\right)=0$

$-\left(x-2\right)\left(x+5\right)=0$

$\left\{{}\begin{matrix}x-2=0\x+5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\x=-5\end{matrix}\right.$

c) $\left(2x-3\right)^2-\left(x+5\right)^2=0$

$\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0$

$\left(x-8\right)\left(3x+2\right)=0$

$\left\{{}\begin{matrix}x-8=0\3x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=8\x=-\dfrac{2}{3}\end{matrix}\right.$

d) $x^3+x^2-4x-4=0$

$x^2\left(x+1\right)-4\left(x+1\right)=0$

$\left(x+1\right)\left(x^2-4\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)=0$

$\Rightarrow\left\{{}\begin{matrix}x+1=0\x-2=0\x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-1\x=2\x=-2\end{matrix}\right.$

g) $\left(x-1\right)\left(2x+3-x\right)=0$

$\left(x-1\right)\left(x+3\right)=0$

$\Rightarrow\left\{{}\begin{matrix}x-1=0\x+3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\x=-3\end{matrix}\right.$

h) $x^2-4x+8-2x+1=x^2-6x+9=0$

$\left(x-3\right)^2=0\Rightarrow x=3$

Câu trả lời: