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a) \(\left(x+5\right)^2=100\Leftrightarrow\orbr{\begin{cases}\left(x+5\right)^2=10^2\\\left(x+5\right)^2=\left(-10\right)^2\end{cases}\Leftrightarrow\orbr{\begin{cases}x+5=10\\x+5=-10\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=5\\x=-15\end{cases}}}\)
b) \(\left(2x-4\right)^2=0\Leftrightarrow2x-4=0\Leftrightarrow2x=4\Leftrightarrow x=2\)
c) \(\left(x-1\right)^3=27\Leftrightarrow\left(x-1\right)^3=3^3\Leftrightarrow x-1=3\Leftrightarrow x=4\)
a) \(\left(x+5\right)^2=100\)
=> \(\orbr{\begin{cases}\left(x+5\right)^2=10^2\\\left(x+5\right)^2=\left(-10\right)^2\end{cases}}\)
=> \(\orbr{\begin{cases}x+5=10\\x+5=-10\end{cases}}\)
=> \(\orbr{\begin{cases}x=5\\x=-15\end{cases}}\)
b) \(\left(2x-4\right)^2=0\)
=> \(2x-4=0\)
=> \(2x=4\)
=> \(x=2\)
c) \(\left(x-1\right)^3=27\)
=> \(\left(x-1\right)^3=3^3\)
=> \(x-1=3\)
=> \(x=4\)
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\(a,3^n=3^4\)
\(\Rightarrow n=4\)
\(b,2008^n=2008^0\)
\(\Rightarrow n=0\)
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\(4^x=64\)
\(\Rightarrow x=3\)
\(15^x=225\)
\(\Rightarrow x=2\)
\(3^x:9=27\)
\(\Leftrightarrow3^x=243\)
\(\Leftrightarrow x=5\)
\(x^{2018}=0\)
\(\Leftrightarrow x=0\)
\(x^{50}=x\)
\(\Rightarrow x\in\left\{0;1\right\}\)
\(300^x=1\)
\(\Rightarrow x=0\)
`\(12^x=144\)
\(\Rightarrow x=2\)
4x=64=43=> x=3
15x=225=152=> x=2
3x :9 = 27
3x=33x32=35=> x=5
X2018=0=> x=0
X50=x=> x=1 hoặc 0
300x=1=> x=0
12x=144=122=> x=2
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\(\left(x-3\right)\left(x-12\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-12=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=12\end{cases}}\)
\(\Rightarrow x\in\left\{3;12\right\}\)
\(\left(x^2-81\right)\left(x^2+9\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^2-81=0\\x^2+9=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=9\\x\in\varnothing\end{cases}}\Leftrightarrow x=9\)
\(\Rightarrow x=9\)
\(\left(x-4\right)\left(x+2\right)< 0\)
\(\Rightarrow\hept{\begin{cases}x-4\\x+2\end{cases}}\)trái dấu
\(TH1:\hept{\begin{cases}x-4>0\\x+2< 0\end{cases}}\Leftrightarrow\hept{\begin{cases}x>4\\x< -2\end{cases}}\Leftrightarrow x\in\varnothing\)
\(TH2:\hept{\begin{cases}x-4< 0\\x+2>0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x< 4\\x>-2\end{cases}}\Leftrightarrow x\in\left\{-1;0;1;2;3\right\}\)
Vậy \(x\in\left\{-1;0;1;2;3\right\}\)
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1.
a) ( 57 + 59 ) . ( 68 + 610 ) . ( 24 - 42 )
= ( 57 + 59 ) . ( 68 + 610 ) . 0
= 0
b) 9 < 3x < 27
32 < 3x < 33
2 < x < 3
Vậy 2 < x < 3
2.
a) xy - 2x = 0
x ( y - 2 ) = 0
\(\Rightarrow\orbr{\begin{cases}x=0\\y-2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\y=2\end{cases}}}\)
b) ( x- 4 ) . ( x - 3 ) = 0
\(\Rightarrow\orbr{\begin{cases}x-4=0\\x-3=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=4\\x=3\end{cases}}\)
c) Ta có : 3n+2 + 3n = 3n . 32 + 3n = 3n . ( 32 + 1 ) = 3n . 10 \(⋮\)10
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\orbr{\frac{\begin{cases}x^4-16=0=>x^4=2^4=>x=+-2\\3^{2x-1}-27=0=>2x-1=3=>x=2\end{cases}}{ }}\)
DS x={-2,2}