Question

Answer 1

a: \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{5}{2}\\x_1x_2=\dfrac{3}{2}\end{matrix}\right.\)

\(A=2\left(x_1^2+x_2^2\right)-x_1x_2=2\left[\left(x_1+x_2\right)^2\right]-5x_1x_2\)

\(=2\cdot\dfrac{25}{4}-5\cdot\dfrac{3}{2}=5\)

b: \(B=\left(x_1+x_2\right)\left(x_1-x_2\right)\)

\(=\dfrac{5}{2}\cdot\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}\)

\(=\dfrac{5}{2}\cdot\sqrt{\dfrac{25}{4}-4\cdot\dfrac{3}{2}}=\dfrac{5}{4}\)