Question

if a²+a+1=0 find(1-a+a²) (1+a-à²)​

Answer 1

Answer:

Since formula for a^3 -b^3 = (a-b) (a^2 +ab +b^2)

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therefore,

a^3 -1 = (a-1)(a^2 +a +1) =(a-1) (0) =0

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a^3= 1. ---------( i )

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Since given that a^2 +a+1 =0,

hence, a+1 = -a^2 --------(ii)

and a^2 +1 = -a. --------(iii)

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Now,

(1-a+ a^2) (1+a- a^2)= (a^2 +1 -a) (1+a - a^2) = (-a -a) (-a^2 -a^2)

{from equations ii and iii}

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therefore,

(1-a+ a^2) (1+a- a^2) = (-2a) (-2 a^2) = 4 (a^3)

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from i, we know that a^3=1,

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Hence, (1-a+ a^2) (1+a- a^2)= 4×1 = 4.