x^3 +27+(x+3)(x-9)=0
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a) \(x+546=46\\ x=46-546\\ x=-500\)
b) \(2x-19\times3=27\\ 2x-57=27\\ 2x=27+57\\ 2x=84\\ x=84:2\\ x=42\)
c) \(x+12=23+3\times3^4\\ x+12=23+3\times81\\ x=23+243-12\\ x=254\)
d) \(x-12=3-3\times2^4\\ x-12=3-3\times16\\ x=3-48+12\\ x=-33\)
e) \(\left(27-x\right)\left(x+9\right)=0\\ \Rightarrow\left[{}\begin{matrix}27-x=0\\x+9=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=27\\x=-9\end{matrix}\right.\)
f) \(\left(-x\right)\left(x-43\right)=0\\ \Rightarrow\left[{}\begin{matrix}-x=0\\x-43=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=43\end{matrix}\right.\)
x^3+27+(x+3)(x-9)=0
(x+3)(x^2-3x+9)+(x+3)(x-9)=0
(x+3)(x^2-3x+9+x-9)=0
(x+3)(x^2-2x)=0
(x+3)x(x-2)=0
suy ra x+3=0 hoặc x=0 hoặc x-2=0
x=-3 hoặc x=0 hoặc x=2
=x3+33+(x+3)(x-9)
=(x+3)(x2-3x+9)+(x+3)(x-9)
=(x+3)(x2-3x+9+x-9)
=(x+3)(x2-2x)
=(x+3)(x-2)x
\(\left(y-2\right)\left(y-3\right)+\left(y-2\right)-1=0\)
\(\Leftrightarrow\left(y-2\right)\left(y-3\right)+\left(y-3\right)=0\)
\(\Leftrightarrow\left(y-3\right)^2=0\)
\(\Leftrightarrow y=3\)
\(x^3+27+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-2x\right)=0\)
\(\Leftrightarrow\left(x+3\right)x\left(x-2\right)=0\)
\(\Leftrightarrow x\in\left\{0;-3;2\right\}\)
Câu a :
\(3x\left(x-1\right)+\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(3x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x+1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
Vậy \(x=1\) hoặc \(x=-\dfrac{1}{3}\)
Câu b :
\(x^3+27+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
\(\Leftrightarrow x\left(x+3\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+3=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=2\end{matrix}\right.\)
Vậy ................
x3 + 27 + (x + 3)(x - 9) = 0
(x + 3)(x2 - 3x + 9) + (x + 3)(x - 9) = 0
(x + 3)(x2 - 3x + 9 + x - 9) = 0
(x + 3)(x2 - 2x) = 0
x(x + 3)(x - 2) = 0
\(\left[\begin{array}{nghiempt}x=0\\x+3=0\\x-2=0\end{array}\right.\)
\(\left[\begin{array}{nghiempt}x=0\\x=-3\\x=2\end{array}\right.\)
=>\(\left(x^3+3^3\right)+\left(x+3\right)\left(x-9\right)=0\)
=>\(\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
=>\(\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
=>\(\left(x+3\right)\left(x^2-2x\right)=0\)
=>\(\left(x+3\right)x\left(x-2\right)=0\)
.........
tu tinh nhe
Vậy x=-3,x=0,x=2