If alpha beta are roots px2+qx+r=0 then find alpha cube+beta cube & alpha square beta+alpha beta square
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Answer:
α³ + β³ = (3pqr -q³)/p³
α²β + αβ² = -qr/p²
Step-by-step explanation:
alpha beta are roots px2+qx+r=0
α + β = -q/p ( sum of roots)
αβ = r/p ( products of Roots)
α³ + β³ = (α + β)³ -3αβ(α + β)
=> α³ + β³ = (-q/p)³ -3(r/p)(-q/p)
=> α³ + β³ = -(q/p)³ + 3qr/p²
=> α³ + β³ = (1/p³)(-q³ + 3pqr)
=> α³ + β³ = (3pqr -q³)/p³
α²β + αβ² = αβ(β + α)
=> α²β + αβ² = (r/p)(-q/p)
=> α²β + αβ² = -qr/p²
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