If alpha and beta be the roots of equation x^2-x+1=0, then alpha^2009 + beta^2009 is equal to?          [Ans: 1]

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Please find below the solution to the asked query:

x2-x+1=0By Shridharacharya's formula, we havex=1±1-42=1±-32=1±i32=1+i32 or 1-i32=--1-i32 or --1+i32=-ω2 or -ωHenceα=-ω and β=-ω2Also we know thatω3n=1 and1+ω+ω2=1..iα2009+β2009=α2007.α2+β2007.β2 2007 is a multiple of 3=-ω2007 -ω2+-ω22007 -ω22=-ω2007 ω2-ω22007 ω4=-1.ω2-1.ω3.ω=-ω2-ωUsing i we get=1 Answer

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