1: \(x_1+x_2=-\dfrac{b}{a}=5;x_1x_2=\dfrac{c}{a}=-3\)
\(-2x_1x_2^2-2x_1^2\cdot x_2\)
\(=-2x_1x_2\left(x_1+x_2\right)\)
\(=-2\cdot\left(-3\right)\cdot5=6\cdot5=30\)
2: \(\dfrac{x_1+3}{x_2}+\dfrac{x_2+3}{x_1}\)
\(=\dfrac{x_1^2+3x_1+x_2^2+3x_2}{x_1x_2}\)
\(=\dfrac{\left(x_1^2+x_2^2\right)+3\left(x_1+x_2\right)}{x_1x_2}\)
\(=\dfrac{\left(x_1+x_2\right)^2-2x_1x_2+3\left(x_1+x_2\right)}{x_1x_2}\)
\(=\dfrac{5^2-2\cdot\left(-3\right)+3\cdot5}{-3}=\dfrac{25+15+6}{-3}=\dfrac{-46}{3}\)
3: \(-3x_1^2-3x_2^2\)
\(=-3\left(x_1^2+x_2^2\right)\)
\(=-3\left[\left(x_1+x_2\right)^2-2x_1x_2\right]\)
\(=-3\left[5^2-2\cdot\left(-3\right)\right]=-3\cdot31=-93\)
