a) \(x^2-36=0\)
\(\Rightarrow x^2-6^2=0\)
\(\Rightarrow\left(x-6\right)\left(x+6\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-6=0\\x+6=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6\\x=-6\end{matrix}\right.\)
b) \(x^3-0,25x=0\)
\(\Rightarrow x\left(x^2-0,25\right)=0\)
\(\Rightarrow x\left[x^2-\left(0,5\right)^2\right]=0\)
\(\Rightarrow x\left(x-0,5\right)\left(x+0,5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x-0,5=0\\x+0,5=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=0,5\\x=-0,5\end{matrix}\right.\)
c) \(x^2-10x=-25\)
\(\Rightarrow x^2-10x+25=0\)
\(\Rightarrow x^2-2\cdot x\cdot5+5^2=0\)
\(\Rightarrow\left(x-5\right)^2=0\)
\(\Rightarrow x-5=0\)
\(\Rightarrow x=5\)
d) \(x^2-2x=-1\) (sửa đề)
\(\Rightarrow x^2-2x+1=0\)
\(\Rightarrow\left(x-1\right)^2=0\)
\(\Rightarrow x-1=0\)
\(\Rightarrow x=1\)
e) \(x^3+3x^2=-3x-1\)
\(\Rightarrow x^3+3x^2+3x+1=0\)
\(\Rightarrow\left(x+1\right)^3=0\)
\(\Rightarrow x+1=0\)
\(\Rightarrow x=-1\)
\(\text{#}Toru\)
a: \(x^2-36=0\)
=>\(x^2=36=6^2\)
=>\(\left[{}\begin{matrix}x=6\\x=-6\end{matrix}\right.\)
b: \(x^3-0,25x=0\)
=>\(x\left(x^2-0,25\right)=0\)
=>\(x\left(x-0,5\right)\left(x+0,5\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-0,5=0\\x+0,5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=0,5\\x=-0,5\end{matrix}\right.\)
c: \(x^2-10x=-25\)
=>\(x^2-10x+25=0\)
=>\(\left(x-5\right)^2=0\)
=>x-5=0
=>x=5
e: \(x^3+3x^2=-3x-1\)
=>\(x^3+3x^2+3x+1=0\)
=>\(\left(x+1\right)^3=0\)
=>x+1=0
=>x=-1
