1-if-s-n-n-n-n-where-are-the-root-of-ax-3-bx-2-cx-d-0-then-show-that-s-4-4abd-4b-2-c-2c-a-3-

Question Number 43665 by peter frank last updated on 13/Sep/18

1) i f s_{n} = α^{n} + β^{n} + λ^{n} w h e r e α, β, λ

a r e t h e r o o t o f {a x}^{3} + {b x}^{2} + c x + d = 0

t h e n s h o w t h a t s_{4} = \frac{4 a b d + 4 b^{2} c - 2 c}{a^{3}}

Commented by math1967 last updated on 14/Sep/18

m o r e c o n d i t i o n r e q u i r e, I t h i n k

Answered by MJS last updated on 15/Sep/18

{let}^{'} s try an example with given values

2 (x - 3) (x + 5) (x - 7) = 0

2 x^{3} - 10 x^{2} - 58 x + 210 = 0

3^{4} + {(- 5)}^{4} + 7^{4} = 3107

\frac{4 \times 2 \times (- 10) \times 210 + 4 \times {(- 10)}^{2} (- 58) - 2 (- 58)}{2^{3}} = - 4985.5

\Rightarrow not true

Commented by math1967 last updated on 15/Sep/18

Y o u a r e c o r r e c t s i r