Question

if α and β are the zeroes of 3x²-2x-21,find the value of α³ + β³

Answer 1

Solution:

》given eq is :- 3x²-2x-21

》α+ β = -b/a = 2/3

》αβ = c/a = -21/3 = -7
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》α²+ β²=(α + β)²-2αβ

》α²+ β²=(2/3)²-2×(-7) =4/9+14=(56+9)/126

》= 65/126

》α³ + β³ = (α + β)(α²+ β²-αβ)

》α³ + β³ = (2/3)×(65/126-2/3)

》= 2/3×(65-84)/126

》= -38/378

》α³ + β³ = -19/189 ans