Question

$x_{1} x_{2}$ корни уравнения $2 x^{2} - 9x - 12=0$. не решая уравнения найдите:

а)$x_{1} ^{2} x_{2} + x_{1} x_{2} ^{2}$

б)$frac{x_{2} }{x_{1} } + frac{ x_{1}}{ x_{2}}$

в)$x_{1}^{3} + x_{2}^{3}$

Answer 1

x1*x2=-6
x1+x2=4,5
a) x1x2(x2+x2)=-6(4,5)=-27
b) (x2^2+x1^2)/x1x2=((x1+x2)^2-2x1x2)/x1x2=(4,5^2+12)/-6=-5,375
c) x1^3+x2^2=(x1+x2)(x1^2+x2^2-x1x2)=4,5(4,5^2+18)=172,125