Question

cho PT 2x² - 9x +1 =0 không giải PT tính

1,x₁x₂² + x₂x₁²

^{2, \(\dfrac{1}{x_{1^{ }}^3}\)}+\(\dfrac{1}{x_{2^{ }}^3}\)

Answer 1

áp dụng hệ thức vi ét ta có : \(\left\{{}\begin{matrix}x_1+x_2=\dfrac{9}{2}\\x_1x_2=\dfrac{1}{2}\end{matrix}\right.\)

1) \(x_1x_2^2+x_2x_1^2=x_1x_2\left(x_1+x_2\right)\) (1)

thay vào ta có : (1) \(\Leftrightarrow\) \(\dfrac{9}{2}.\dfrac{1}{2}=\dfrac{9}{4}\) vậy \(x_1x_2^2+x_2x_1^2=\dfrac{9}{4}\)

2) \(\dfrac{1}{x_1^3}+\dfrac{1}{x_2^2}\) = \(\dfrac{x_1^3+x^3_2}{\left(x_1x_2\right)^3}\) = \(\dfrac{\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)}{\left(x_1x_2\right)^3}\) (2)

thay vào ta có : (2) \(\Leftrightarrow\) \(\dfrac{\left(\dfrac{9}{2}\right)^3-3\left(\dfrac{1}{2}\right)\left(\dfrac{9}{2}\right)}{\left(\dfrac{1}{2}\right)^3}\)

= \(675\)