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\(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-19\)
\(\Rightarrow x^3+2x^2+x+x^2+2x+1-x\left(x^2-2x+1\right)+\left(x^2-2x+1\right)-6x^2+12x-6=-19\)
\(\Rightarrow x^3+2x^2+x+x^2+2x+1-x\left(x^2-2x+1\right)+x^2-2x+1-6x^2+12x-6=-19\)
\(\Rightarrow x^3-2x^2+13x-4-x\left(x^2-2x+1\right)=-19\)
\(\Rightarrow x^3-2x^2+13x-4-x^3+2x^2-x=-19\)
\(\Rightarrow12x-4=-19\)
\(\Rightarrow12x=-15\)
\(\Rightarrow x=\frac{-5}{4}\)
<=> 2x^2 - 2.2x.1 + 1^2 - 3( x^2 + x - x -1 ) + (-x^2) + 2.-x.3 + 3^2 = 2x^2 + 20x + 17
<=> 2x^2 - 4x + 1 - 3x^2 - 3x + 3x + 3 + (-x^2) + (-6x) + 3^2 = 2x^2 + 20x + 17
<=> ___________________________________________- 2x^2 - 20x - 17
<=> -2x^2 - 10x- 13
<=> a = - 2 ; b = - 10 ; c = -13
1)
\(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-19\)
\(\Leftrightarrow x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)-6\left(x^2-2x+1\right)=-19\)
\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+12x-6+19=0\)
\(\Leftrightarrow\left(x^3-x^3\right)+\left(3x^2+3x^2-6x^2\right)+\left(3x-3x+12x\right)+\left(1+1-6+19\right)=0\)
\(\Leftrightarrow12x+15=0\)
\(\Leftrightarrow x=-\frac{5}{4}\)
(x + 1)(x2 - x + 1) - x(x2 - 2) = 19
<=> x3 - x2 + x + x2 - x + 1 - x3 + 2x = 19
<=> 2x + 1 = 19
<=> 2x = 19 - 1
<=> 2x = 18
<=> x = 9
=> x = 9
\(\left(x+1\right)\left(x^2-x+1\right)-x\left(x^2-2\right)=19\)
\(\Leftrightarrow x^3-x^2+x+x^2-x+1-x^3+2x=19\)
\(\Leftrightarrow2x+1=19\)
\(\Leftrightarrow2x=19-1\)
\(\Leftrightarrow2x=18\Leftrightarrow x=\frac{18}{2}=9\)