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Bài 4:
a: xy=-2
=>\(x\cdot y=1\cdot\left(-2\right)=\left(-2\right)\cdot1=\left(-1\right)\cdot2=2\cdot\left(-1\right)\)
=>\(\left(x,y\right)\in\left\{\left(1;-2\right);\left(-2;1\right);\left(-1;2\right);\left(2;-1\right)\right\}\)
b: \(\left(x-1\right)\left(y+2\right)=-3\)
=>\(\left(x-1\right)\cdot\left(y+2\right)=1\cdot\left(-3\right)=\left(-3\right)\cdot1=-1\cdot3=3\cdot\left(-1\right)\)
=>\(\left(x-1;y+2\right)\in\left\{\left(1;-3\right);\left(-3;1\right);\left(-1;3\right);\left(3;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(2;-5\right);\left(-2;-1\right);\left(0;1\right);\left(4;-3\right)\right\}\)
Bài 3:
a: \(x\left(x+9\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x+9=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=0\\x=-9\end{matrix}\right.\)
b: \(\left(x-5\right)^2=9\)
=>\(\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=3+5=8\\x=-3+5=2\end{matrix}\right.\)
c: \(\left(7-x\right)^2=-64\)
mà \(\left(7-x\right)^2>=0\forall x\)
nên \(x\in\varnothing\)
Bài 2:
a: \(\left(-31\right)\cdot x=-93\)
=>\(31\cdot x=93\)
=>\(x=\dfrac{93}{31}=3\)
b: \(\left(-4\right)\cdot x=-20\)
=>\(4\cdot x=20\)
=>\(x=\dfrac{20}{4}=5\)
c: \(5x+1=-4\)
=>\(5x=-4-1=-5\)
=>\(x=-\dfrac{5}{5}=-1\)
d: \(-12x+1=-4\)
=>\(-12x=-4-1=-5\)
=>\(12x=5\)
=>\(x=\dfrac{5}{12}\)
e: =>-40+3+33+40-x=47
=>36-x=47
=>x=-11
f: =>x(x-3)(11-x)(11+x)=0
hay \(x\in\left\{0;3;11;-11\right\}\)
g: =>-62-38-x+2x=-100
=>x-100=-100
hay x=0
i: =>x-12-2x-31=6
=>-x-43=6
=>x+43=-6
hay x=-49
h: =>(x+1)=0
=>x=-1
f: =>x(x-3)(x+11)(x-11)=0
hay \(x\in\left\{0;3;-11;11\right\}\)
a)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\Leftrightarrow x\left(x-1\right)^{x+2}\left(x-2\right)=0\)
Do đó \(x\in\left\{0;1;2\right\}\)
b)
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot...\cdot\frac{31}{64}=2^x\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{4\cdot6\cdot8\cdot...\cdot64}=2^x\Leftrightarrow\frac{31!}{\left(2\cdot2\right)\cdot\left(2\cdot3\right)\cdot\left(2\cdot4\right)\cdot...\cdot\left(2\cdot31\right)\cdot64}=2^x\)
\(\frac{31!}{2^{30}\cdot31!\cdot2^6}=2^x\Leftrightarrow\frac{1}{2^{36}}=2^x\Leftrightarrow2^{-36}=2^x\Rightarrow x=-36\)
\(-3+x=5-\left(-7\right)\)
\(\Leftrightarrow-3+x=5+7\)
\(\Leftrightarrow-3+x=12\)
\(\Leftrightarrow x=12+3\)
\(\Leftrightarrow x=15\)
Vậy x= 15
\(x-2=2x-7\)
\(\Leftrightarrow x-2+7=2x\)
\(\Leftrightarrow x-\left(2-7\right)=2x\)
\(\Leftrightarrow2-7=x-2x\)
\(\Leftrightarrow-5=-x\)
\(\Leftrightarrow x=5\)
Vậy x= 5
56 . Tính nhanh :
a ) 2 x 31 x 12 + 4 x 6 x 42 + 8 x 27 x 3
b ) 36 x 28 + 36 x 82 + 64 x 69 + 64 x 41
a) 2 x 31 x 12 + 4 x 6 x 42 + 8 x 27 x 3
= 24 x 31 + 24 x 42 + 24 x 27
= 21 x ( 31 + 42 + 27)
= 21 x 100
= 2100
b) 36 x 28 + 36 x 82 + 64 x 69 + 64 x 41
= 36 x ( 28 + 82) + 64 x ( 69 + 41)
= 36 x 110 + 64 x 110
= 110 x ( 36 + 64)
= 110 x 100
= 11000
a) \(56-\left(x+31\right)=12\)
\(\Rightarrow x+31=44\)
\(\Rightarrow x=13\)
b) \(\left(2x+5\right)\cdot4=6^2\)
\(\Rightarrow2x+5=9\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2\)
a) 56 - ( x+31) = 12
\(\Rightarrow\) -x + 25 = 12
\(\Rightarrow\) -x = -13
\(\Rightarrow\) x = 13
b) ( 2x +5 ) . 4=62
\(\Leftrightarrow\) (2x + 5) . 4 = 36
\(\Rightarrow\) 2x + 5 = 9
\(\Rightarrow\) 2x = 4
\(\Rightarrow\) x = 2