if alpha and beta are zeroes of p(x)=x^2-x-1. find the value of alpha cube +beta cube.

Question

if alpha and beta are zeroes of p(x)=x^2-x-1. find the value of alpha cube +beta cube.

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Alexandra 3 weeks 2021-09-07T06:20:19+00:00 1 Answer 0 views 0

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    2021-09-07T06:21:59+00:00

    Alpha = a & beta = b

    Answer:

    4

    Step-by-step explanation:

    Polynomials written in form of x^2 – Sx + P, represent S as sum of roots anf P as product of roots.

    So, here,

    Sum = a + b = 1

    Product = ab = – 1

    = > a + b = 1

    Cube on both sides –

    = > ( a + b )³ = 1³

    = > a³ + b³ + 3ab( a + b ) = 1

    = > a³ + b³ + 3(product)(sum) = 1

    = > a³ + b³ + 3(-1)(1) = 1

    = > a³ + b³ – 3 = 1

    = > a³ + b³ = 1+ 3

    = > + = 4

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