1) if s_(n ) =α^n +β^n +λ^(n ) where α,β,λ are the root of ax^3 +bx^2 +cx+d=0 then show that s


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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

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