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a, 12- (-4)= 16
b, 12- (-14)= 26
c, (-13)-(-5)=-8
d, (-2)-(-10)= 8
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\(\left(2x+3\right)^3=\left(-25\right).\left(-5\right)\)
\(\Leftrightarrow\left(2x+3\right)^3=125\)
\(\Leftrightarrow\left(2x+3\right)^3=5^3\)
\(\Leftrightarrow2x+3=5\)
\(\Leftrightarrow2x=2\)
\(\Leftrightarrow x=1\)
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\(\Leftrightarrow x\left(y+1\right)+y+1=31\\ \Leftrightarrow\left(x+1\right)\left(y+1\right)=31=31\cdot1\)
\(TH_1:\left\{{}\begin{matrix}x+1=31\\y+1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=30\\y=0\end{matrix}\right.\rightarrow\left(30;0\right)\\ TH_2:\left\{{}\begin{matrix}x+1=1\\y+1=31\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=30\end{matrix}\right.\rightarrow\left(0;30\right)\)
Vậy \(\left(x;y\right)\in\left\{\left(30;0\right);\left(0;30\right)\right\}\)
\(\Leftrightarrow xy+x+y+1=31\Leftrightarrow\left(x+1\right)\left(y+1\right)=31\)
Do x, y nguyên dương nên xảy ra các TH sau:
TH1: \(\left\{{}\begin{matrix}x+1=1\\y+1=31\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=30\end{matrix}\right.\)(LOẠI)
TH2:\(\left\{{}\begin{matrix}x+1=31\\y+1=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=30\\y=0\end{matrix}\right.\)(LOẠI)
Vậy không có x, y nguyên dương thoả mãn đề bài.
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\(C=\left(x-5\right)^2+10\)
Ta có: \(\left(x-5\right)^2\ge0\forall x\)
\(\Rightarrow C=\left(x-5\right)^2+10\ge10\forall x\)
Dấu \("="\) xảy ra khi: \(x-5=0\Leftrightarrow x=5\)
Vậy \(Min_C=10\) khi \(x=5\).
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a ) Ta có : - 12 . ( x - 5 ) + 7( 3 - x ) = 5
Suy ra - 12x - ( - 12 ) . 5 + 7 . 3 - 7x = 5
Suy ra - 12x + 60 + 21 - 7x = 5
Suy ra - 12x - 7x = 5 - 60 - 21
Suy ra - 19x = - 76
Suy ra x = -76 : ( - 19 )
Vậy x = 4
b ) Ta có : 30 . ( x + 2 ) - 6 . ( x - 5 ) - 24x = 100
Suy ra 30x + 30 . 2 - 6x - ( - 6 ) . 5 - 24x = 100
Suy ra 30x + 60 - 6x + 30 - 24x = 100
Suy ra 30x - 6x - 24x = 100 - 60 - 30
Suy ra 0x = 10
Vậy x = 0
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Tính nhanh:
a) 36.(65-79)+65|35-79|
=36.(-14) + 65.44
=-504 + 2860
=2356
b) 12.(34-86)+34.(86-12)+86.(12-34)-12.(34+86)
= 12.(-52) +34.74+86. (-22) - 12.120
=-624 + 2516 +(-1892) -1440
= 1892 + (-1892) -1440
=0- 1440
=-1440
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a)\(-17+\left|5-x\right|=10\)
\(\Leftrightarrow\left|5-x\right|=10-\left(-17\right)\)
\(\Leftrightarrow\left|5-x\right|=10+17\)
\(\Leftrightarrow\left|5-x\right|=27\)
\(\Leftrightarrow\orbr{\begin{cases}5-x=27\\5-x=-27\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=-22\\x=32\end{cases}}\)
b) \(45-5\left|12-x\right|=125\div\left(-25\right)\)
\(\Leftrightarrow45-5\left|12-x\right|=-5\)
\(\Leftrightarrow5\left|12-x\right|=45-\left(-5\right)\)
\(\Leftrightarrow5\left|12-x\right|=45+5\)
\(\Leftrightarrow5\left|12-x\right|=50\)
\(\Leftrightarrow\left|12-x\right|=10\)
\(\Leftrightarrow\orbr{\begin{cases}12-x=10\\12-x=-10\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=22\end{cases}}\)
c) \(2< \left|3-x\right|\le5\)
\(\Leftrightarrow\left|3-x\right|\in\left\{3;4;5\right\}\)
* \(\left|3-x\right|=3\Leftrightarrow\orbr{\begin{cases}3-x=3\\3-x=-3\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=6\end{cases}}}\)
* \(\left|3-x\right|=4\Leftrightarrow\orbr{\begin{cases}3-x=4\\3-x=-4\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=7\end{cases}}}\)
* \(\left|3-x\right|=5\Leftrightarrow\orbr{\begin{cases}3-x=5\\3-x=-5\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=8\end{cases}}}\)
d) \(\left|x+4\right|< 3\)
mà \(\left|x+4\right|\ge0\)
\(\Rightarrow\left|x+4\right|\in\left\{0;1;2\right\}\)
* \(\left|x+4\right|=0\Leftrightarrow x+4=0\Leftrightarrow x=-4\)
* \(\left|x+4\right|=1\Leftrightarrow\orbr{\begin{cases}x+4=1\\x+4=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-3\\x=-5\end{cases}}}\)
* \(\left|x+4\right|=2\Leftrightarrow\orbr{\begin{cases}x+4=2\\x+4=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=-6\end{cases}}}\)
(-12).x+34=10
(-12) . x = 10 - 34
(-12) . x = -24
x = (-24) : (-12)
x = 2
HT và $$$
[-12].x=10-34
[-12].x=-24
x=-24:[-12]
x=-2