Letr, sandt be the three roots of the equation 8x3 + 1001x + 2008 = 0. Find the
value of 1001–(r-s)^3 – (s+t)^3-(t+r)^3 divided by 8
Answers
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Step-by-step explanation:
We have,
f(x)=8x
3
+1001x+2008=0
f(x)=8x
3
+0x
2
+1001x+2008=0
(r+s)
3
+(s+t)
3
+(t+r)
3
=(−t)
3
+(−r)
3
+(−s)
3
=−(t
3
+r
3
+s
3
)
But we can get,
r
3
+s
3
+t
3
=(r+s+t)(r
2
+s
2
+t
2
−rs−st−tr)+3rst
⇒r
3
+s
3
+t
3
=0+3(−251)=−753
Now,
(r+s)
3
+(s+t)
3
+(t+r)
3
=753
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