toán 8: tính A, A = 2x + 3 + /-3x/ khi x<0
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a: (2x-3)(3x+6)>0
=>(2x-3)(x+2)>0
=>x<-2 hoặc x>3/2
b: (3x+4)(2x-6)<0
=>(3x+4)(x-3)<0
=>-4/3<x<3
c: (3x+5)(2x+4)>4
\(\Leftrightarrow6x^2+12x+10x+20-4>0\)
\(\Leftrightarrow6x^2+22x+16>0\)
=>\(6x^2+6x+16x+16>0\)
=>(x+1)(3x+8)>0
=>x>-1 hoặc x<-8/3
f: (4x-8)(2x+5)<0
=>(x-2)(2x+5)<0
=>-5/2<x<2
h: (3x-7)(x+1)<=0
=>x+1>=0 và 3x-7<=0
=>-1<=x<=7/3
Bài 1
a, 32.(-64) - 64. 68
= -64.(32 + 68)
= -64 .100
= - 6400
b, -54.76 + 12.(-76) - 76.34
= -76.(54 + 12 + 34)
= -76.100
= -7600
19- 42.(-19) + 38.5
= 19 + 42.19 + 19.2.5
= 19.(1 + 42 + 10)
= 19.53
= 1007
a)Tử: \(x^5-2x^4+2x^3-4x^2-3x+6\)
\(=x^5+2x^3-3x-2x^4-4x^2+6\)
\(=x\left(x^4+2x^2-3\right)-2\left(x^4+2x^2-3\right)\)
\(=\left(x-2\right)\left(x^4+2x^2-3\right)\)
\(=\left(x-2\right)\left[x^4-x^2+3x^2-3\right]\)
\(=\left(x-2\right)\left[x^2\left(x^2-1\right)+3\left(x^2-1\right)\right]\)
\(=\left(x-2\right)\left(x^2-1\right)\left(x^2+3\right)\)
\(=\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x^2+3\right)\)
Mẫu: \(x^2+2x-8=x^2-2x+4x-8\)
\(=x\left(x-2\right)+4\left(x-2\right)\)
\(=\left(x-2\right)\left(x+4\right)\)
Suy ra \(A=\dfrac{\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x^2+3\right)}{\left(x-2\right)\left(x+4\right)}=\dfrac{\left(x-1\right)\left(x+1\right)\left(x^2+3\right)}{x+4}\)
b)\(A=0\Rightarrow\dfrac{\left(x-1\right)\left(x+1\right)\left(x^2+3\right)}{x+4}=0\)
\(\Rightarrow\left(x-1\right)\left(x+1\right)\left(x^2+3\right)=0\)
Dễ thấy: \(x^2+3\ge3>0\forall x\) (vô nghiệm)
Nên \(\left[{}\begin{matrix}x-1=0\\x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
A có nghĩa khi \(x+4\ne0\Rightarrow x\ne-4\)
A vô nghĩa khi \(x+4=0\Rightarrow x=-4\)
a) Liệt kê
x = {-7;-6;-5;-4;-3;-2;-1;0;1;2;3;4;5;6;7}
Tính tổng là: -7+-6+-5+-4+.....+4+5+6+7
= (-7+7)+(-6+6)+(-5+5)+....+(-1+1)+0
= 0+0+0....+0
= 0
b) Liệt kê
x = {-5;-4;-3;-2;-1;0;1;2;3}
Tính tổng: -5+-4+-3+-2+-2+0+1+2+3
= (-3+3)+(-2+2)+(-1+1)+0+-5+-4
= 0+0+0+0+ -9
= -9
c) Liệt kê:
x = { -19;-18;-17;-16;....;18;19;20}
Tính tổng: -19+-18+-17+-16+....+15+16+17+18+19+20
= (-19+19)+(-18+18)+...+(-1+1)+0+20
= 0 + 0+...+0+20
= 20
*TÌM X:
a) 2x -35 = 15
2x = 15 + 35
2x = 50
x = 50 :2
x = 25
b) 3x + 17 = 2
3x = 17+2
3x = 19
x = 19 : 3
x = 6,33
c) /x-1/ = 0
\(\hept{\begin{cases}x-1=0\\x-1=-0\left(loai\right)\end{cases}}\)
Vậy x-1 = 0
x = 0 +1 = 1
Bài 2:
a: \(\Leftrightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
a: \(A=4x-3x^2+20-15x-9x^2-12x-4+\left(2x+1\right)^3-\left(8x^3-1\right)\)
\(=-12x^2-23x+16+8x^3+12x^2+6x+1-8x^3+1\)
\(=-17x+18\)
Khi \(x< 0\)thì \(-3x>0\)\(\Rightarrow\left|-3x\right|=-3x\)
Ta có: \(A=2x+3+\left(-3x\right)=-x+3\)