Algebra

Simplifying the equation, we have \(x^2 + 6x - 2  = 0 \)

In the form mx^2 + nx + p  = 0, the Product of the roots ab = -n/m =   -2  

So 2ab = -4

Sum of the roots a + b =  p/m =  -6     

Squaring both sides, we have 

\(a^2 + b^2 + 2ab = 36 \\ a^2 + b^2 - 4 =36 \\ a^2 + b^2  = 40 \)

\(1/a^3  + 1/b^3  = \\(a^3 + b^3) / (ab)^3   \)        Note  :  a^3 + b^3 = (a + b) (a^2 + b^2 - ab)

So we have

\((a + b) ( a^2 + b^2 -ab)  / (ab)^3  = \\ (-6) (40 - -2) / (-8)   =  \\ (6) (42 / 8)  =   31.5 \)

Thus, the answer is 31.5

Thanks! :)