Question

Answer 1

a) \(\left(3x-1\right)\left(2x+7\right)+\left(x+1\right)\left(5-6x\right)=16\)

    \(6x^2+21x-2x-7+5x-6x^2+5-6x=16\)

    \(18x=18\)

    \(x=1\)

b) \(\left(x^4+3x^3+9x-9\right):\left(x^2+3\right)=-3\)

    \(x^4+3x^3+9x-9=-3x^2-9\)

    \(x^4+3x^3+3x^2+9x=0\)

    \(x\left(x^3+3x^2+3x+9\right)=0\)

    \(x\left(x+3\right)\left(x^2+3\right)=0\)  \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\)

c) \(\left(x+1\right)\left(x^2-x+1\right)-x\left(x-3\right)\left(x+3\right)=8\)

    \(x^3-x^2+x+x^2-x+1-x^3-9x=8\)

    \(9x=7\)

    \(x=\dfrac{7}{9}\)