Tìm x biết :
a ) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
b ) \(2x^2+7x+3\) = 0
c ) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
d ) \(2x^2+11x+9=0\)
e ) \(x\left(x+2\right)-x^2-8=0\)
f ) \(\left(x-3\right)\left(x^2+3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
a) \(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
\(\Rightarrow x^3+3^3-x\left(x^2-4\right)=27\)
\(\Rightarrow x^3+27-x^3+4x=27\)
\(\Rightarrow27+4x=27\)
\(\Rightarrow4x=0\)
\(\Rightarrow x=0\)
b) \(2x^2+7x+3=0\)
\(\Rightarrow2x^2+x+6x+3=0\)
\(\Rightarrow x\left(2x+1\right)+3\left(2x+1\right)=0\)
\(\Rightarrow\left(2x+1\right)\left(x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x+1=0\\x+3=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=-1\\x=-3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{2}\\x=-3\end{matrix}\right.\)
c) Trùng đề bài a
d) \(2x^2+11x+9=0\)
\(\Rightarrow2x^2+2x+9x+9=0\)
\(\Rightarrow2x\left(x+1\right)+9\left(x+1\right)=0\)
\(\Rightarrow\left(x+1\right)\left(2x+9\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\2x+9=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\2x=-9\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{9}{2}\end{matrix}\right.\)
e) \(x\left(x+2\right)-x^2-8=0\)
\(\Rightarrow x^2+2x-x^2-8=0\)
\(\Rightarrow2x-8=0\)
\(\Rightarrow2\left(x-4\right)=0\)
\(\Rightarrow x-4=0\)
\(\Rightarrow x=4\)
f) \(\left(x-3\right)\left(x^2+3x+9\right)-x\left(x-2\right)\left(x+2\right)=27\)
\(\Rightarrow x^3-3^3-x\left(x^2-4\right)=27\)
\(\Rightarrow x^3-27-x^3+4x=27\)
\(\Rightarrow-27+4x=27\)
\(\Rightarrow4x=27+27=54\)
\(\Rightarrow x=\dfrac{54}{4}=\dfrac{27}{2}\)