Bài 3: Nhân, chia số hữu tỉ

\(\left(x+1\right)\left(x+2\right)\left(x+3\right)-x^3-8x\left(x+2\right)=6\\ \Leftrightarrow\left(x^2+3x+2\right).\left(x+3\right)-x^3-8x^2-16x=6\\ \Leftrightarrow x^3+6x^2+11x+6-x^3-8x^2-16x-6=0\\ \Leftrightarrow-2x^2-5x=0\\ \Leftrightarrow x.\left(-2x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\-2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{5}{2}\end{matrix}\right.\)

\(\left(4x^2-3\right)^3+8=0\)

\(\left(4x^2-3\right)^3=-8\\ =>4x^2-3=-2\)

\(4x^2=1\\ x^2=\dfrac{1}{4}=>\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)

\(=\dfrac{3^2\left(2^2+2^3+1\right)}{-13}=\dfrac{-13\cdot3^2}{13}=-9\)

=-4/5(25+3/19-35-3/19)

=-4/5*(-10)

=8

\(25\dfrac{3}{19}:\left(-\dfrac{5}{4}\right)-35\dfrac{3}{19}:\left(-\dfrac{5}{4}\right)\\ =\left(25\dfrac{3}{19}-35\dfrac{3}{19}\right):\left(-\dfrac{5}{4}\right)\\ =-10:\left(-\dfrac{5}{4}\right)\\ =8\)

a> Để A là số nguyên thì x-2+5 chia hết cho x-2

=>\(x-2\in\left\{1;-1;5;-5\right\}\)

hay \(x\in\left\{3;1;7;-3\right\}\)

b: Để B là số nguyên thì -2x-6+7 chia hết cho x+3

=>\(x+3\in\left\{1;-1;7;-7\right\}\)

hay \(x\in\left\{-2;-4;4;-10\right\}\)

Lời giải:
$-Q=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+....+\frac{5}{97.99}$

$-Q=\frac{5}{2}(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99})$

$=\frac{5}{2}(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{99})$

$=\frac{5}{2}(1-\frac{1}{99})=\frac{245}{99}$

$\Rightarrow Q=\frac{-245}{99}$

5:

a: =>2x=0,2

=>x=0,1

b: =>(x-1,6)=13/6*12/13=2

=>x=3,6

c: =>x-3/2=0 hoặc 2x+1=0

=>x=3/2 hoặc x=-1/2

d: =>7^m=7 hoặc 7^m=49

=>m=1; m=2

\(\dfrac{5}{3}x+\dfrac{1}{3}x=\dfrac{5}{7}-\dfrac{2}{3}< =>2x=\dfrac{1}{21}< =>\dfrac{1}{42}\)

`2^x+3-3.2=-92`

`=>2^x+3-6=-92`

`=>2^x+3=-92+6`

`=>2^x+3= -86`

`=>2^x=-86 -3`

`=>2^x=-89`

`->` đề sai ko bn

a) \(\dfrac{2}{5}.x-1=-4x\)

     \(-1=-4x-\dfrac{2}{5}.x\\\)

     \(x.\left(-4-\dfrac{2}{5}\right)=-1\)

     \(x.\dfrac{-22}{5}=-1\)

     \(x=-1:\dfrac{-22}{5}\)

     \(x=\dfrac{5}{22}\)

b) \(3.\left(\dfrac{1}{2}x-1\right)=-x+1\)

    \(3.\dfrac{1}{2}x-3=-x+1\)

    \(-3=-x+1-3.\dfrac{1}{2}x\)

    \(x.\left(-1\right)+1-3.\dfrac{1}{2}x=-3\)

    \(x.\left(-1-3.\dfrac{1}{2}\right)+1=-3\)

    \(x.\dfrac{-5}{2}+1=-3\)

    \(x.\dfrac{-5}{2}=-3-1\)

    \(x.\dfrac{-5}{2}=-4\)

    \(x=-4:\left(\dfrac{-5}{2}\right)\)

    \(x=\dfrac{8}{5}\)