Bài 12: Tính chất của phép nhân

a ) 48 - 73 + |15| - ( - 29 ) 

= -25 + 15 + 29 = 19

b) 134 + 46.( 39 - 78 ) - | 267 |

= 134 + 46.( -39 ) -  267 = -133 -1794 = -1927

c) 36 - 16.( -2 )² + ( - 53 )

= 36 - 16.4 - 53 = -17 - 64 = -81

d) ( 259 - 47 - 5 ) - ( 259 - 5 )

= 259 - 47 - 5 - 259 + 5  = - 5 + 5 + 259 - 259 = 0

e ) 325. 26 - 325 . 125 - 325 

= 325 (26 - 125 - 1) = 325. (-100) = -32500

a, Ta có: |x| \(\ge\) 0 với mọi x

|x + 1| \(\ge\) 0 với mọi x

|x + 2| \(\ge\) 0 với mọi x

|x + 3| \(\ge\) 0 với mọi x

\(\Rightarrow\) |x| + |x + 1| + |x + 2| + |x + 3| \(\ge\) 0 với mọi x

hay 6x \(\ge\) 0 

\(\Rightarrow\) x \(\ge\) 0 (đpcm)

b, Vì x \(\ge\) 0 nên

|x| + |x + 1| + |x + 2| + |x + 3| = 6x

\(\Rightarrow\) x + x + 1 + x + 2 + x + 3 = 6x

\(\Rightarrow\) 2x = 6

\(\Rightarrow\) x = 3 (TM)

Vậy x = 3

Chúc bn học tốt!

(x-2) . (y+1) = -2

\(\Rightarrow\) (x-2) và (y+1) là U(-2)

Mà U(-2) = {1; -1; 2; -2}

Nên\(\left\{{}\begin{matrix}x-2=1\\y+1=2\end{matrix}\right.\)        \(\Rightarrow\)         \(\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)

      \(\left\{{}\begin{matrix}x-2=-1\\y+1=-2\end{matrix}\right.\)      \(\Rightarrow\)         \(\left\{{}\begin{matrix}x=1\\y=-3\end{matrix}\right.\)

(x-2) . (y+1) = -2

Ta có: -2 = 1.2; 2.1; -1.(-2); -2.(-1)

Lập bảng

Vậy:

       */ Nếu y = -3 thì x = 3

       */ Nếu y = 0 thì x = 0

       */ Nếu y = -2 thì x = 4

       */ Nếu y = 1 thì x = 1

2,180

b) Ta có: (-x)+14=12

\(\Leftrightarrow-x+14=12\)

\(\Leftrightarrow-x=12-14=-2\)

hay x=2

Vậy: x=2

-x = 12 - 14

-x = -2

\(\Rightarrow\)x = 2

-x = 12 - 14

-x = -2

$\Rightarrow$x = 2

-30 + x=13

x=13+30

x=43

a) Ta có: (-30)-(-x)=13

\(\Leftrightarrow-30+x=13\)

\(\Leftrightarrow x-30=13\)

\(\Leftrightarrow x=13+30=43\)

Vậy: x=43

-30 + x=13

x=13+30

x=43

Câu 1: 

a) Ta có: x-3 là ước của 13

\(\Leftrightarrow x-3\inƯ\left(13\right)\)

\(\Leftrightarrow x-3\in\left\{1;-1;13;-13\right\}\)

hay \(x\in\left\{4;2;16;-10\right\}\)(thỏa mãn)

Vậy: \(x\in\left\{4;2;16;-10\right\}\)

b) Ta có: \(x^2-7\) là ước của \(x^2+2\)

\(\Leftrightarrow x^2+2⋮x^2-7\)

\(\Leftrightarrow x^2-7+9⋮x^2-7\)

mà \(x^2-7⋮x^2-7\)

nên \(9⋮x^2-7\)

\(\Leftrightarrow x^2-7\inƯ\left(9\right)\)

\(\Leftrightarrow x^2-7\in\left\{1;-1;3;-3;9;-9\right\}\)

mà \(x^2-7\ge-7\forall x\)

nên \(x^2-7\in\left\{1;-1;3;-3;9\right\}\)

\(\Leftrightarrow x^2\in\left\{8;6;10;4;16\right\}\)

\(\Leftrightarrow x\in\left\{2\sqrt{2};-2\sqrt{2};-\sqrt{6};\sqrt{6};\sqrt{10};-\sqrt{10};2;-2;4;-4\right\}\)

mà \(x\in Z\)

nên \(x\in\left\{2;-2;4;-4\right\}\)

Vậy: \(x\in\left\{2;-2;4;-4\right\}\)

Câu 2: 

a) Ta có: \(2\left(x-3\right)-3\left(x-5\right)=4\left(3-x\right)-18\)

\(\Leftrightarrow2x-6-3x+15=12-4x-18\)

\(\Leftrightarrow-x+9+4x+6=0\)

\(\Leftrightarrow3x+15=0\)

\(\Leftrightarrow3x=-15\)

hay x=-5

Vậy: x=-5

Ta có: 3(x+1)=x+6

\(\Leftrightarrow3x+3-x-6=0\)

\(\Leftrightarrow2x-3=0\)

\(\Leftrightarrow2x=3\)

hay \(x=\dfrac{3}{2}\)

Vậy: \(x=\dfrac{3}{2}\)

3(\(x\)+1)=x+6

⇒3\(x\)+3=\(x\)+6

⇒3\(x\)+3-\(x\)+6=0

⇒2\(x\)-3=0

⇒2\(x\)=3

     \(x\)=\(\dfrac{3}{2}\)

vậy \(x=\dfrac{3}{2}\)

\(x^2-xy+y+2=0\)

\(\Leftrightarrow\left(x-\dfrac{y}{2}\right)^2-\left(\dfrac{y}{2}-1\right)^2+3=0\)

\(\Leftrightarrow\left(x-\dfrac{y}{2}\right)^2-\left(\dfrac{y}{2}-1\right)^2=1-4\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-\dfrac{y}{2}\right)^2=1\\\left(\dfrac{y}{2}-1\right)^2=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}2x-y=2\\2x-y=-2\end{matrix}\right.\\\left[{}\begin{matrix}y=6\\y=-2\end{matrix}\right.\end{matrix}\right.\)

với y=6 \(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)

với y=-2 \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)

vậy S=\(\left\{\left(4;6\right);\left(2;6\right);\left(0;-2\right);\left(-2;-2\right)\right\}\)

_là gì vậy?

136 . 23 + 136 . 17 - 40 . 36

= 136(23 + 17) - 40 . 36

= 136 . 40 - 40 . 36

= 40(136 - 36) = 40 . 100 = 4000

\(136.23+136.17-40.36=136\left(23+17\right)-40.36\)

\(=136.40-40.36=40.\left(136-36\right)\)

\(=40.100=400\)