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a) <=> (8-5x+x-2)(x+2) + 4(x^2-x-2)=0
<=> 6x +12 - 4x^2 - 8x +4x^2 -4x -8 =0
<=> -6x -4 = 0
<=> x= 4/6

A = \(4\left(x-5\right)-x^2\left(x+1\right)-x^3\left(x-3\right)-\left(x-4+x^2\right)\)
A = \(4x-20-x^3-x^2-x^4+3x^3-x+4-x^2\)
A = \(-x^3-3x^3-x^2+x^2-x^4+4x-x-20+4\)
A = \(-4x^3-x^4+4x-16\)
B = \(-3\left(x^2-x+1\right)-2\left(4-x^2\right)-6\left(x+1\right)-x^4-x^3\)
B = \(-3x^2+3x-3-8+2x^2-6x-6-x^4-x^3\)
B = \(-x^4-x^3-3x^2-2x^2+3x-6x-3-8-6\)
B = \(-x^4-x^3-5x^2-3x-17\)
C = \(-\left(x^4+3x^2-2\right)-x^2\left(5-x\right)+3\left(x-1\right)\)
C = \(-x^4-3x^2+2-5x^2+x^3+3x-3\)
C = \(-x^4+x^3-3x^2+5x^2+3x+2-3\)
C = \(-x^4+x^3-2x^2+3x-1\)
#Yiin
\(A=4x-20-x^3-x-x^4+3x^3-x+4-x^2\)
\(=-x^4+2x^3-x^2+2x-16\)
\(B=-3x^2+3x-3-8+2x^2-6x-6-x^4-x^3\)
\(=-x^4-x^3-x^2-3x-17\)
\(C=-x^4-3x^2+2-5x^2+x^3+3x-3\)
\(=-x^4+x^3-8x^2+3x-1\)
Từ đó có:
\(A-B=-x^4+2x^3-x^2+2x-16-\left(-x^4-x^3-x^2-3x-17\right)\)
\(=-x^4+2x^3-x^2+2x-16+x^4+x^3+x^2+3x+17\)\(=3x^3+5x+1\)
\(B-C=-x^4-x^3-x^2-3x-17-\left(-x^4+x^3-8x^2+3x-1\right)\)
\(=-x^4-x^3-x^2-3x-17+x^4-x^3+8x^2-3x+1\)
\(=-2x^3+7x^2-6x-16\)
\(C-A=-x^4+x^3-8x^2+3x-1-\left(-x^4+2x^3-x^2-2x-16\right)\)
\(=-x^4+x^3-8x^2+3x-1+x^4-2x^3+x^2+2x+16\)
\(=-x^3-7x^2+5x+15\)

2.
a. \(A=\left(a+b-c\right)-\left(2a+b-2c\right)\)
\(=a+b-c-2a-b+2c\)
\(=-a+c\)
Thay a=-1 ; c=1 vào A ta có:
\(A=-\left(-1\right)+1=1+1=2\)
Vậy A = 2 với a=-1 ; c = 1
b. \(B=a-\left[\left(a-3\right)+\left(a+3\right)-\left(a-2\right)\right]\)
\(=a-\left(a-3+a+3-a+2\right)\)
\(=a-a+3-a-3+a-2\)
\(=\left(a-a-a+a\right)+\left(3-3-2\right)\)
\(=-2\)
Vậy B = -2

Ta có : A = 1.2 + 2.3 + 3.4 + ...... + 100.101
=> 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 100.101.102
=> 3A = 100.101.102
=> A = 100.101.102/3
=> A = 343400

Bài 2:
a: \(x^2+2>=2\)
\(\Leftrightarrow\dfrac{8}{x^2+2}< =4\)
\(\Leftrightarrow B>=-4\)
Dấu '=' xảy ra khi x=0
b: \(4+2\left(x-2\right)^2>=4\)
=>C=1/4+2(x-2)^2<=1/4
Dấu '=' xảy ra khi x=2
Bài 3:
a: \(\Leftrightarrow\dfrac{x+5-x+3}{x-3}< 0\)
=>x-3<0
=>x<3
b: \(\Leftrightarrow\dfrac{x+3-2x-8}{x+4}>0\)
\(\Leftrightarrow\dfrac{-x-5}{x+4}>0\)
=>(x+5)/(x+4)<0
=>-5<x<-4
a, <=> |x| = 1,427
<=> x=1,427 hoặc x= -1,427
b, <=> |x+1/3| = 5
<=> x+1/3= 5 hoặc x+1/3 = -5
<=> x= 14/3 hoặc x= -16/3
a) đúng
b) sai