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b) \(27x^3-54x^2+36x=8\)
\(\Rightarrow27x^3-54x^2+36x-8=0\)
\(\Rightarrow\left(3x\right)^3-3.\left(3x\right)^2.2+3.3x.2^2-2^3=0\)
\(\Rightarrow\left(3x-2\right)^3=0\)
\(\Rightarrow3x-2=0\)
\(\Rightarrow3x=2\)
\(\Rightarrow x=\dfrac{2}{3}\)
(2x-5)^2-(5+2x)^2=0
<=>(2x-5-5-2x)(2x-5+5+2x)=0
<=>(-10).(4x)=0
<=>(-40x)=0
<=>x =0
27x^3-54x^2+36x=8
<=>27x^3-54x^2+36x-8=0
<=>(3x-2)^3=0
<=>3x-2=0
<=>3x=2
<=>x=2/3
\(6x^2-9xy+10x-15y\\ =3x\left(2x-3y\right)+5\left(2x-3y\right)\\ =\left(3x+5\right)\left(2x-3y\right)\\ 27x^3+36x^2y+12xy^2\\ =3x\left(9x^2+12xy+4y^2\right)\\ =3x\left(3x+2y\right)^2\)
a) \(6x^2-9xy+10x-15y=\left(6x^2-9xy\right)+\left(10x-15y\right)\)
\(=3x\left(2x-3y\right)+5\left(2x-3y\right)\)
\(=\left(3x+5\right)\left(2x-3y\right)\)
b) \(27x^3+36x^2y+12xy^2=3x\left(9x^2+12xy+4y^2\right)\)
\(=3x\left[\left(3x\right)^2+2\cdot3x\cdot2y+\left(2y\right)^2\right]\)
\(=3x\left(3x+2y\right)^2\)
\(\)
\(a,\Rightarrow4x\left(x^2-9\right)=0\\ \Rightarrow4x\left(x-3\right)\left(x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\\ b,\Rightarrow\left(3x-5-x-1\right)\left(3x-5+x+1\right)=0\\ \Rightarrow\left(2x-6\right)\left(4x-4\right)=0\\ \Rightarrow2\left(x-3\right)4\left(x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
a) \(\Rightarrow4x\left(x^2-9\right)=0\)
\(\Rightarrow4x\left(x-3\right)\left(x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=3\\x=-3\end{matrix}\right.\)
b) \(\Rightarrow\left(3x-5-x-1\right)\left(3x-5+x+1\right)=0\)
\(\Rightarrow\left(2x-6\right)\left(4x-4\right)=0\)
\(\Rightarrow8\left(x-3\right)\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
+(x-3)2-x2=11
x2-6x+9-x2=11
-6x+9=11
-6x=2
x=2:-6
x=-1/3
(6x-3)2-36x(x-1)=40
36x2-36x+9-36x2+36x=40
9=40
=> đề sai
(2-x)2-7(x2+11)=0
4-4x+x2-7x2-77=0
-73-4x-6x2
ht bt
\(8-36x+54x^2-27x^3=0\)
\(=2^3-3.2^2.3x+3.9x^2.2-3x^3\)
\(=2-3x^3=0\)
\(\Rightarrow2-3x=0\Rightarrow x=\frac{2}{3}\)
Bài 2:
a: \(A=a^2+b^2+c^2+2ab-2ac-2bc+a^2+b^2+c^2-2ab-2bc+2ac\)
\(=2a^2+2b^2+2c^2-4bc\)
\(=2+2\cdot9+2\cdot1-4\cdot3\cdot\left(-1\right)=22+12=34\)
b: \(B=\left(a+b-a+b\right)\left(a+b+a-b\right)=4ab=4\cdot2\cdot5=40\)
\(x^2+x+\dfrac{1}{4}=\left(x+\dfrac{1}{4}\right)^2\)
\(8x^3+27=\left(2x+3\right)\left(4x^2-6x+9\right)\)
\(-x^3+3x^2-3x+1=\left(-x+1\right)^3\)
\(36x^2-12x-36x^2+27x=30\)
\(\Leftrightarrow-12x+27x=30\)
\(\Leftrightarrow15x=30\)
\(\Leftrightarrow x=2\)
36x2-12x-36x2+27x=30
=>(36x2-36x2)-12x+27x=30
=>0-12x+27x=30
=>-12x+27x=30
=>15x=30
=>x=30:15
=>x=2