\(1.\left(x-1\right)^2=4=\left(-2\right)^2=2^2\)
\(TH1:x-1=2\Rightarrow x=3\)
\(TH2:x-1=-2\Rightarrow x=-1\)
Vậy:...
\(2.\left(1+x\right)^2=9=\left(-3\right)^2=3^2\)
\(TH1:1+x=3\Rightarrow x=2\)
\(TH2:1+x=-3\Rightarrow x=-4\)
Vậy:....
\(3,\left(x+2019\right)^4=1\Rightarrow\left(x+2019\right)^4=1^4\)
\(\Rightarrow\orbr{\begin{cases}x+2019=1\\x+2019=-1\end{cases}\Rightarrow\orbr{\begin{cases}x=-2018\\x=-2020\end{cases}}}\)
\(4,\left(x+10\right)^3=1\Rightarrow\left(x+10\right)^3=1^3\)
\(\Rightarrow x+10=1\)
\(\Rightarrow x=-9\)
\(5.\left(x-20\right)^3=-1=\left(-1\right)^3\)
\(\Rightarrow x-20=-1\Rightarrow x=19\)
Vậy:....
\(6.x^4:x^2=4\)
\(x^2=4=2^2=\left(-2\right)^2\)
\(\Rightarrow x=2,x=-2\)
Vậy:....
-Hok tốt ~
1) \(\left(x-1\right)^2-4=0\)
\(\Rightarrow\left(x-1\right)^2=4\)
\(\Rightarrow\orbr{\begin{cases}\left(x-1\right)^2=2^2\\\left(x-1\right)^2=\left(-2\right)^2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-1=2\\x-1=\left(-2\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=3\\x=-1\end{cases}}\)
Vậy x=3 hoặc x= -1
2 ) \(\left(1+x\right)^2-\left(-3\right)^2=0\)
\(\Rightarrow\left(1+x\right)^2-9=0\)
\(\Rightarrow\left(1+x\right)^2=9\)
\(\Rightarrow\orbr{\begin{cases}\left(1+x\right)^2=3^2\\\left(1+x\right)^2=\left(-3\right)^2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}1+x=3\\1+x=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-4\end{cases}}\)
Vậy x=2 hoặc x=-4
3) \(\left(x+2019\right)^4=1\)
\(\Rightarrow\orbr{\begin{cases}\left(x+2019\right)^4=1^4\\\left(x+2019\right)^4=\left(-1\right)^4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x+2019=1\\x+2019=\left(-1\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-2018\\x=-2020\end{cases}}\)
Vậy x = -2018 hoặc x = -2020
4 )\(\left(x+10\right)^3=1\)
\(\Rightarrow\left(x+10\right)^3=1^3\)
\(\Rightarrow x+10=1\)
\(\Rightarrow x=-9\)
Vậy x= -9
5)\(\left(x-20\right)^3+1=0\)
\(\Rightarrow\left(x-20\right)^{^{ }3}=\left(-1\right)\)
\(\Rightarrow\left(x-20\right)^3=\left(-1\right)^3\)
\(\Rightarrow x-20=-1\)
\(\Rightarrow x=-19\)
Vậy x= -19
6) \(x^4=4x^2\)
\(\Rightarrow x^2.x^2-4x^2=0\)
\(\Rightarrow x^2.\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x^2=0\\x^2-4=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^2=4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=2hoặcx=-2\end{cases}}\)
Vậy x=0 hoặc x=2 hoặc x=-2
#học tốt