Question

Answer 1

Áp dụng hệ thức Vi - et, ta có:

\(\left\{{}\begin{matrix}x_1+x_2=\dfrac{5}{3}\\x_1x_2=\dfrac{-15}{3}=-5\end{matrix}\right.\)

a) 

\(A=x_1\left(1-x_2\right)+x_2\left(1-x_1\right)\\ =x_1-x_1x_2+x_2-x_1x_2\\ =\left(x_1+x_2\right)-2x_1x_2\\ =\dfrac{5}{3}-2.\left(-5\right)=\dfrac{35}{3}\)

b) 

\(B=x_1^2+x_2^2-x_1x_2\\ =\left(x_1+x_2\right)^2-3x_1x_2\\ =\left(\dfrac{5}{3}\right)^2-3.\left(-5\right)=\dfrac{160}{9}\)

c) 

\(C=x_1-x_2\\ \Rightarrow C^2=\left(x_1-x_2\right)^2\\ =\left(x_1+x_2\right)^2-4x_1x_2\\ =\left(\dfrac{5}{3}\right)^2-4.\left(-5\right)=\dfrac{205}{9}\\ \Rightarrow C=\pm\dfrac{\sqrt{205}}{3}\)