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Let and be two roots of the equation x^{2} + 2x + 2 = 0, the

Question

Let $α$ and $β$ be two roots of the equation $x^{2} + 2 x + 2 = 0$ , then $α^{15} + β^{15}$ is equal to

512

- 512

- 256

256

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Scarlett Discussed

Let

α

and

β

be two roots of the equation

x^{2} + 2 x + 2 = 0

, then

α^{15} + β^{15}

is equal to

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

α, β

are roots of equation

x^{2} + 2 x + 2 = 0

root

= \frac{- 2 \pm 4 - 8}{2} = - 1 \pm i

\Rightarrow α = i - i

and

β = - (1 + i)

\Rightarrow α^{2} = - 2 i

and

β^{2} = 2 i

\Rightarrow α^{14} = (- 2 i)^{7}

and

β^{14} = (2 i)^{7}

\Rightarrow α^{14} = - 128 i^{3}

and

β^{14} = 128 i^{3}

= 128 i

and

= - 128 i

α^{15} = 128 i (i - 1)

and

β^{15} = 128 i (i + 1) = - 128 + 128 i

= - 128 - 128 i

\Rightarrow α^{15} + β^{15} = - 128 - 128 i - 128 + 128 i = - 256

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Question Text	Let $α$ and $β$ be two roots of the equation $x^{2} + 2 x + 2 = 0$ , then $α^{15} + β^{15}$ is equal to
Answer Type	Text solution:1
Upvotes	150