Let `r ,s ,a n dt` be the roots of equation `8x^2+1001 x+2008=0.` Then find the value of .

Answer

753

Explanation

Equation ` 8x^(3) + 1001 x _ 2008 = 0 ` has roots r, s, and t . Thus,
` r + s + r = 0 , rst = - (2008)/(8) = - 251`
Now let ` r + s + = A, s + t = B, t + r = C`
`therefore A + B+ C = 2 (r + s + t) = 0`
Hence ` A^(3) + B(3) + C^(3) = 3ABC`
`therefore (r + s )^(3) + (s + t)^(3) + (t + r)^(3)`
` = 3 (r + s)(s + t)(t + r)`
= ` 3 (r + s + t - t ) (s + t + r - r) (t + r + s - s)`
`= - 3rst (as r + s + t = 0)`
`3 (251) = 753` .