JEE Advance - Mathematics (1978 - No. 6)
If x = a + b, y = a$$\gamma $$ + b$$\beta $$ and z = a$$\beta $$ +b$$\gamma $$ where $$\gamma $$ and $$\beta $$ are the complex cube roots of unity, show that xyz = $${a^3} + {b^3}$$.
The given equation is incorrect; it should be xyz = (a+b)(a^2+b^2).
The statement is true; xyz = a^3 + b^3.
The statement is false; xyz = (a+b)^3.
The statement is conditionally true, requiring a=b for xyz = a^3 + b^3 to hold.
The expression cannot be simplified further without knowing the values of a and b.
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