If ω is imaginary cube root of unity and (a + bω + cω2)2015 = (a + bω2 + cω

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If &#969; is imaginary cube root of unity and (a + b&#969; + c&#969;2)2015 = (a + b&#969;2 + c&#969;) where a,b,c are unequal realnumbers, then a2 + b2 + c2 - ab - bc - ca is equal to -

Accepted Answer

Let a + b&#969; + c&#969;2 = zgiven equation is z2015 = &#8658; |z|2015 = || &#8658; |z |= 0 or 1but |z| = 0 &#8658; a = b = c|z| = 1 &#8658; z = 1&#8658; (a + b&#969; + c&#969;2)(a + b&#969;2&#969; + c&#969;) = 1&#8658; (a2 + b2 + c2 - ab - bc - ca) = 1

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