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a) Ta có :
\(0,\left(27\right)+0,\left(72\right)==\dfrac{27}{99}+\dfrac{72}{99}=\dfrac{99}{99}=1\)
\(\Rightarrow0,\left(27\right)+0,\left(72\right)=1\rightarrowđpcm\)
b) Ta có :
\(0,\left(22\right).\dfrac{9}{2}=\dfrac{2}{9}.\dfrac{9}{2}=\dfrac{18}{18}=1\)
\(\Rightarrow0,22.\dfrac{9}{2}=1\rightarrowđpcm\)
c) Ta có :
\(\left[0,\left(11\right).9\right]^{2003}=\left[\dfrac{1}{9}.9\right]^{2003}=\left[\dfrac{9}{9}\right]^{2003}=1^{2003}=1\)
\(\Rightarrow\left[0,\left(11\right).9\right]^{2003}=1\rightarrowđpcm\)
\(a)\dfrac{-4}{9}-\dfrac{5}{9}:x=\dfrac{1}{18}\)
\(\Leftrightarrow\dfrac{5}{9}:x=\dfrac{-8}{18}+\dfrac{-1}{18}\)
\(\Leftrightarrow\dfrac{5}{9}:x=\dfrac{-1}{2}\)
\(\Leftrightarrow x=\dfrac{5}{9}.\left(-2\right)\)
\(\Leftrightarrow x=\dfrac{-10}{9}\)
\(b)\left|x\right|=\dfrac{1}{2}\)
\(\Leftrightarrow x\in\left\{-\dfrac{1}{2};\dfrac{1}{2}\right\}\)
\(c)x\left(x-\dfrac{1}{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-\dfrac{1}{3}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\end{matrix}\right.\)
\(\Leftrightarrow x\in\left\{0;\dfrac{1}{3}\right\}\)
a) x=\(\dfrac{-10}{9}\)
b)x∈{\(\dfrac{1}{2}\); \(\dfrac{-1}{2}\)}
a) \(\left(x-4\right)\left(x^2+1\right)=0\)
\(\Rightarrow\) Có 2 trường hợp:
1) x - 4 = 0 \(\Rightarrow\)x = 4
2) \(x^2+1=0\Rightarrow x^2=-1\) .Mà \(x^2\ge0\forall x\Rightarrow x\in\varnothing\)
Vậy x =4
b) \(3.x^2-4x=0\)
\(\Rightarrow x\left(3x-4\right)=0\Rightarrow\) Có 2 trường hợp:
1) x = 0
2) 3x - 4 = 0 \(\Rightarrow\) 3x = 4 \(\Rightarrow x=\frac{4}{3}\)
Vậy \(x\in\left\{0;\frac{4}{3}\right\}\)
c) \(x^2+9=0\)
\(\Rightarrow x^2=-9\) . Mà \(x^2\ge0\forall x\Rightarrow x\in\varnothing\)
Vậy \(x\varnothing\in\)
Tìm x biết:
a) x^2-3.x=0
b) 2.x^2+5.x=0
c) x^2+1=0
d) x^2-1=0
e) x.(x-3)-x+3=0
g) x^2.(x+2)-9.x-18=0
a)x^2-3.x=0
x^3.(1-3)=0
x^3.(-2)=0
x^3=0:(-2)
x^3=0
x=0
b)2.x^2+5.x=0
x^3.(2+5)=0
x^3.7=0
x^3=0:7
x^3=0
x=0
c)x^2+1=0
x^2=0-1
x^2=(-1)
x ko thỏa mãn
d)x^2-1=0
x^2=0+1
x^2=1
x=1 hoặc x=(-1)
e)x.(x-3)-x+3=0
Mình ko bt xin lỗi
g)x^2.(x+2)-9.x-18=0
x^2.(x+2)-9.x=0+18
x^2.(x+2)-9.x=18
x^2.x+x^2.2-9.x=18
Mk chỉ giải đc đến đây thôi. Xin lỗi!
a/ \(x^2=5\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{5}\\x=-\sqrt{5}\end{matrix}\right.\)
vậy .....
b/ \(x^2-9=0\)
\(\Leftrightarrow x^2=9\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2=3^2\\x^2=\left(-3\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
Vậy .......( nhầm cái ngoặc)
c/ \(x^2+1=0\)
\(\Leftrightarrow x^2=-1\)
Mà \(x^2\ge0\Leftrightarrow x\in\varnothing\)
Vậy ....
d/ \(\left(x-1\right)^2=9\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-1\right)^2=3^2\\\left(x-1\right)^2=\left(-3\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=3\\x-1=-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)
Vậy ...
e/ \(\left(2x+3\right)^2=25\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(2x+3\right)^2=5^2\\\left(2x+3\right)^2=\left(-5\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+3=5\\2x+3=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-4\end{matrix}\right.\)
Vậy .....
f/ Ta có :
\(x^2=1\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=1^2\\x^2=\left(-1\right)^2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Vậy ...
\(x^2=5\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{5}\\x=-\sqrt{5}\end{matrix}\right.\)
\(\left(x-1\right)^2=9\)
\(\Rightarrow\left[{}\begin{matrix}x-1=3\\x-1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-2\end{matrix}\right.\)
\(x^2-9=0\Leftrightarrow x^2=9\Rightarrow\left[{}\begin{matrix}x=3\\x=-3\end{matrix}\right.\)
\(\left(2x+3\right)^2=25\)
\(\Rightarrow\left[{}\begin{matrix}2x+3=5\\2x+3=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-4\end{matrix}\right.\)
\(x^2+1=0\Rightarrow x^2=-1\Rightarrow x\in\varnothing\)
\(x^2=1\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
a) \(x^2=\frac{4}{9}\)
\(\Rightarrow x=\frac{2}{3}\)
b)\(x=0,6\)
a) \(x=\frac{2}{3};x=-\frac{2}{3}\)
b) \(x=0,6;x=-0,6\)
c) \(x=0,5;x=-0,5\)
d)\(x=-1\)