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\(\left(x+3\right)^3-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2-2x+1\right)-3x^2=42\)
\(\Rightarrow x^3+9x^2+27x+27-\left[x\left(9x^2+6x+1\right)\right]+8x^2+1-3x^2=42\)
\(\Rightarrow x^3+9x^2+27x+27-9x^3-6x^2-x+8x^2+1-3x^2=42\)
\(\Rightarrow-8x^3+8x^2+26x+28=42\)
\(\left(x+3\right)^3-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2-2x+1\right)-3x^2=42\)
\(\Rightarrow x^3+9x^2+27x+27-x\left(9x^2+6x+1\right)+8x^3+1-3x^2=42\)
\(\Rightarrow x^3+9x^2+27x+28-9x^3-6x^2-x+8x^3-3x^2=42\)
\(\Rightarrow26x+28=42\)
\(\Rightarrow26x=14\Rightarrow x=\dfrac{7}{13}\)
1> 3x(x-2)-2x(2x-1)=(1-x)(1+x)
⇔\(3x^2\)-6x-\(4x^2\)+2x=1-\(x^2\)
⇔-1\(x^2\) - 4x= 1- \(x^2\)
⇔ -1\(x^2\) -4x+ \(x^2\) = 1
⇔-4x=1
⇔ x = \(\dfrac{-1}{4}\)
a)(x+3)3-x(3x+1)2+(2x+1)(4x2-2x+1-3x2)=54
\(\Rightarrow\)x3+9x2+27x+27-x(9x2+6x+1)+(2x+1)(x2-2x+1)=54
\(\Rightarrow\)x3+9x2+27x+27-9x3-6x2-x+2x3-4x2+2x+x2-2x+1=54
\(\Rightarrow\)-6x3+26x+28=54
\(\Rightarrow\)-6x3+26x=54-28
\(\Rightarrow\)-6x3+26x=26
\(\Rightarrow\)-6x3+26x-26=0
\(\Rightarrow\)-2(3x3+13x+14)
a ) \(3x\left(x-1\right)-x\left(3x-2\right)=5\)
\(\Leftrightarrow3x^2-3x-3x^2+2x=5\)
\(\Leftrightarrow-x=5\)
\(\Leftrightarrow x=-5\)
Vậy phương trình có nghiệm x = - 5 .