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( x - 2 )( x + 2 ) - ( x + 3 )( x2 - 3x + 9 ) = 6x - 27
<=> x2 - 4 - ( x3 + 27 ) = 6x - 27
<=> x2 - 4 - x3 - 27 = 6x - 27
<=> x2 - 4 - x3 - 27 - 6x + 27 = 0
<=> -x3 + x2 - 6x - 4 = 0
Gồi đến đây là chịu :)
\(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x^2-9\right)=27\\ x.x^2-x.3x+x.9-x.x^2+x.9=27\\ x^3-3x^2+9x-x^3+9x=27\\ 3x^2+18x=27\\ 21x^2=27\\ x^2=\dfrac{9}{7}\\ \Rightarrow x=\sqrt{\dfrac{9}{7}}\)
\(\left(y-2\right)\left(y-3\right)+\left(y-2\right)-1=0\)
\(\Leftrightarrow\left(y-2\right)\left(y-3\right)+\left(y-3\right)=0\)
\(\Leftrightarrow\left(y-3\right)^2=0\)
\(\Leftrightarrow y=3\)
\(x^3+27+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-2x\right)=0\)
\(\Leftrightarrow\left(x+3\right)x\left(x-2\right)=0\)
\(\Leftrightarrow x\in\left\{0;-3;2\right\}\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x-3\right)\left(x+3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x^2-2x+6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+3=0\\\left(x-1\right)^2+5=0\left(vô.lí\right)\end{matrix}\right.\\ \Leftrightarrow x=-3\)
\(x^3+27=-x^2+9\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-2x+6\right)=0\)
hay x=-3