Question

по теореме виета алгебра. решите пожалуйста. 

Answer 1

По т. Виета, x1 + x2 = – b/a и x1*x2 = c/a.
Следовательно, x1 + x2 = –5/2 = –2,5 и x1*x2 = –9/2 = –4,5.
Далее, 1/x1^3 + 1/x2^3 =
= (x2^3 + x1^3)/(x1^3*x2^3) =
= (x1 + x2)*(x1^2 – x1*x2 + x2^2)/(x1*x2)^3 =
= -2,5*(6,25 – 11,25 + 20,25)/(–4,5)^3 = 
= 0,418

Answer 2

2x²-5x-9=0
1/(x1)³+1/(x2)³=?
x1+x2=5/2;(x1)²+2x1*x2+(x2)²=(5/2)²
x1*x2=-9/2
1/(x1)³+1/(x2)³=((x1)³+(x2)³)/(x1*x2)³=
(x1+x2)(x1)²-x1*x2+(x2)²)/(-9/2)³=
5/2*((5/2)²-3*(-9/2))/(729/8)=
5/2*(25/4+27/2)*8/729=
5/2*79/4*8/729=
5*79/729=395/729