If x , y , z are cube roots of unity and D = x 2 + y 2 x 2 y 2 z 2 y 2 + z 2 y 2 z 2 x 2 z 2 + x 2 , then the real part of D is:

Question

If x , y , z are cube roots of unity and D = ​ x 2 + y 2 x 2 y 2 ​ z 2 y 2 + z 2 y 2 ​ z 2 x 2 z 2 + x 2 ​ ​ , then the real part of D is:

TestHub · Accepted Answer

Applying R 1 ​ → R 1 ​ − R 2 ​ − R 3 ​ , we get: D = ​ 0 x 2 y 2 ​ − 2 y 2 y 2 + z 2 y 2 ​ − 2 x 2 x 2 z 2 + x 2 ​ ​ = 2 x 2 y 2 z 2 ​ 0 1 1 ​ − 2 y 2 + z 2 1 ​ − 2 1 z 2 + x 2 ​ ​ = 4 x 2 y 2 z 2

Mathematics - Determinant Question with Solution | TestHub

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