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Let r,s and t be the roots of the equati...

Let `r,s` and `t` be the roots of the equation `8x^(3)+1001x+2008=0`. If `99lamda=(r+s)^(3)+(s+t)^(3)+(t+r)^(3)`, the value of `[lamda]` (where [.] denotes the greatest integer function) is ____

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The correct Answer is:
7
We have `4+s+t=0` ……………i
`rs+st+tr=1001/8`………ii
and `rst=-2008/8=-251` ……..iii
Now `(r+s)^(3)+(s+t)^(3)+(t+r)^(3)=(-t)^(3)+(-r)^(3)+(-s)^(3)`
`[:' r+s=t=0]`
`=(t^(3)+r^(3)+s^(3))=-3rst[ :' r+s+t=0]`
`=-(-251)=753`
Now `99lamda=(r+s)^(3)+(s+t)^(3)+(t+r)^(3)=753`
`:.lamda=753/99=7.6`
`:.[lamda]=7`
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