Let `a,binRandabne1."If "6a^(2)+20a+15=0and15b^(2)+20b+6=0` then the value of `(4030b^(3))/(ab^(2)-9(ab+1)^(3))` is _____.

Answer

12

Explanation

From the given relations, we can say that and `(1)/(b)` are the roots of the equation `6x^(2)+20x+15=0`.
`:.a+(1)/(b)=(10)/(3)and(a)/(b)=(5)/(2)`
`(b^(3))/(ab^(2)-9(ab+1)^(3))=(1)/(a.(1)/(b)-9(a+(1)/(b))^(3))`
`=(1)/((5)/(2)+9.(1000)/(27))=(6)/(2015)`