a: \(\left(x-3\right)\left(x^2+3x+9\right)+x\left(x+2\right)\left(2-x\right)=1\)
=>\(x^3-27+x\left(4-x^2\right)=1\)
=>\(x^3-27+4x-x^3=1\)
=>4x-27=1
=>4x=28
=>\(x=\dfrac{28}{4}=7\)
b: \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-19\)
=>\(x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-2x+1\right)=-19\)
=>\(6x^2+2-6x^2+12x-6=-19\)
=>12x-4=-19
=>12x=-15
=>\(x=-\dfrac{15}{12}=-\dfrac{5}{4}\)
a)
\(\left(x-3\right)\left(x^2+3x+9\right)+x\left(x+2\right)\left(2-x\right)=1\\ \Leftrightarrow x^3-3^3+x\left(2^2-x^2\right)=1\\ \Leftrightarrow x^3-27+4x-x^3=1\\ \Leftrightarrow4x-27=1\\ \Leftrightarrow4x=27+1=28\\ \Leftrightarrow x=\dfrac{28}{4}=7\)
b)
\(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-19\\ \Leftrightarrow x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)-6\left(x^2-2x+1\right)=-19\\ \Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+12x-6=-19\\ \Leftrightarrow12x-4=-19\\ \Leftrightarrow12x=-19+4=-15\\ \Leftrightarrow x=\dfrac{-15}{12}=\dfrac{-5}{4}\)
