a^2+a+1=0 then (a^2-a+1)(a+1-a^2)=?
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a^2 + a + 1 = 0
a^2 + a = -1
a(a + 1) = -1
a + 1 = -1/a
i.e, 1/a = -(a + 1) ... (1)
Now,
a^2 + (1/a)^2
= a^2 + [-(a+1)]^2 ... from eq. (1)
= a^2 + a^2 + 2a + 1
= 2(a^2 + a + 1) - 1
As, a^2 + a + 1 = 0
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