X x 2 +X x3=8620
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^3+2\left(x-1\right)^2-2\left(x-1\right)\left(x+1\right)=x^3+x-4-\left(x-7\right)\)
\(\Leftrightarrow x^3+2\left(x^2-2x+1\right)-2\left(x^2-1\right)=x^3+x-4-x+7\)
\(\Leftrightarrow x^3+2x^2-4x+2-2x^2+2=x^3+3\)
\(\Leftrightarrow x^3-x^3-4x+2+2+3=0\)
\(\Leftrightarrow-4x+7=0\)
\(\Leftrightarrow x=\frac{7}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,x^3+x^2+x+1=0\\ \Rightarrow x^2\left(x+1\right)+\left(x+1\right)=0\\ \Rightarrow\left(x^2+1\right)\left(x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x^2=-1\left(vô.lí\right)\\x=-1\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{-1\right\}\)
\(b,x^3+x^2-x-1=0\\ \Rightarrow x^2\left(x+1\right)-\left(x+1\right)=0\\ \Rightarrow\left(x^2-1\right)\left(x+1\right)=0\\ \Rightarrow\left(x-1\right)\left(x+1\right)^2=0\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{-1;1\right\}\)
\(c,\left(x+1\right)^2\left(x+2\right)+\left(x+1\right)^2\left(x-2\right)=-24\\ \Rightarrow\left(x+1\right)^2\left(x+2+x-2\right)=-24\\ \Rightarrow2x\left(x^2+2x+1\right)=-24\\ \Rightarrow x^3+2x^2+x+12=0\\ \Rightarrow\left(x^3+3x^2\right)-\left(x^2+3x\right)+\left(4x+12\right)=0\\ \Rightarrow x^2\left(x+3\right)-x\left(x+3\right)+4\left(x+3\right)=0\\ \Rightarrow\left(x^2-x+4\right)\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}\left(x-\dfrac{1}{2}\right)^2+\dfrac{15}{4}=0\left(vô.lí\right)\\x=-3\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{-3\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
`P(x)=\(4x^2+x^3-2x+3-x-x^3+3x-2x^2\)
`= (x^3-x^3)+(4x^2-2x^2)+(-2x-x+3x)+3`
`= 2x^2+3`
`Q(x)=`\(3x^2-3x+2-x^3+2x-x^2\)
`= -x^3+(3x^2-x^2)+(-3x+2x)+2`
`= -x^3+2x^2-x+2`
`P(x)-Q(x)-R(x)=0`
`-> P(X)-Q(x)=R(x)`
`-> R(x)=P(x)-Q(x)`
`-> R(x)=(2x^2+3)-(-x^3+2x^2-x+2)`
`-> R(x)=2x^2+3+x^3-2x^2+x-2`
`= x^3+(2x^2-2x^2)+x+(3-2)`
`= x^3+x+1`
`@`\(\text{dn inactive.}\)
a: P(x)-Q(x)-R(x)=0
=>R(x)=P(x)-Q(x)
=2x^2+3+x^3-2x^2+x-2
=x^3+x+1
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,=x+x^2-x^3+x^4-x^5+1+x-x^2+x^3-x^4-x-x^2+x^3-x^4+x^5+1+x-x^2+x^3-x^4\\ =2x-2x^2+2x^3-2x^4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 4:
\(=\dfrac{a\left(a-b\right)-c\left(a-b\right)}{a\left(a+b\right)-c\left(a+b\right)}=\dfrac{a-b}{a+b}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 1:
b: ĐKXĐ: \(x\notin\left\{3;-3\right\}\)
\(\dfrac{1}{x-3}-\dfrac{1}{x+3}+\dfrac{2x}{9-x^2}\)
\(=\dfrac{1}{x-3}-\dfrac{1}{x+3}-\dfrac{2x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{x+3-x+3-2x}{\left(x-3\right)\left(x+3\right)}=\dfrac{-2x+6}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{-2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=-\dfrac{2}{x+3}\)
c: ĐKXĐ: \(x\notin\left\{2;0\right\}\)
Sửa đề: \(\dfrac{x+1}{x-2}+\dfrac{4-5x}{x^3+4x}:\dfrac{x-2}{x^2+4}\)
\(=\dfrac{x+1}{x-2}+\dfrac{4-5x}{x\left(x^2+4\right)}\cdot\dfrac{x^2+4}{x-2}\)
\(=\dfrac{x+1}{x-2}+\dfrac{4-5x}{x\left(x-2\right)}\)
\(=\dfrac{x\left(x+1\right)+4-5x}{x\left(x-2\right)}=\dfrac{x^2+x-5x+4}{x\left(x-2\right)}\)
\(=\dfrac{x^2-4x+4}{x\left(x-2\right)}=\dfrac{\left(x-2\right)^2}{x\left(x-2\right)}=\dfrac{x-2}{x}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
câu 4: b, đề bài là tính giá trị của A tại x =-1/2;y=-1
Tk
Bài 2
a) F(x)-G(x)+H(x)= \(x^3-2x^2+3x+1-\left(x^3+x-1\right)+\left(2x^2-1\right)\)
= \(x^3-2x^2+3x+1-x^3-x+1+2x^2-1\)
= \(x^3-x^3-2x^2+2x^2+3x-x+1+1-1\)
= 2x + 1
b) 2x + 1 = 0
2x = -1
x=\(\dfrac{-1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=x+x^2-x^3+x^4-x^5+2+2x-2x^2+2x^3-2x^4-\left(1+x+x^2+x^3+x^4-x-x^2-x^3-x^4-x^5\right)\\ =2+3x-x^2+x^3-x^4-x^5-1\\ =-x^5-x^4+x^3-x^2+3x+1\)
x.2+x.3=8620
x.(2+3)=8620
x.5=8620
x 8620:5=4310
Hok tốt!
@Kaito Kid