Let A ={x:x3+1=0};B={x:x2-x+1=0} .Find A n (intersection) B when (i) x is real (ii) x is not real.

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Please find below the solution to the asked query:

We have:A=x:x3+1=0B=x:x2-x+1=0Intersection will consist of common point, hence to get intersection of two sets, put:x3+1=x2-x+1x+1x2-x+1=x2-x+1x+1x2-x+1-x2-x+1=0x2-x+1x+1-1=0x2-x+1x=0casei x is realDiscriminant of x2-x+1 is negative 1-2-4=-3, hence it cannot be 0.x=0HenceAB= 0 x2-x+1x=0Caseii x is not real.x2-x+1=0By Shridharacharya's formula, we have:x=--1±-12-4112=1±1-42=1±-32=1±i32x=1+i32 or 1-i32AB=1+i32,1-i32

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