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Here, w is a cube root of unity

Expert replies
by sanju09 » Tue Jan 12, 2010 4:47 am
Given the following three equations

a w^2 + b + c w = x

a + b w + c w^2 = y

a w + b w^2 + c = z

What is the value of x^3 + y^3 + z^3 - 3 x y z. {Here, w is a cube root of unity.}
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
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Source: — Problem Solving |

by mwmah » Sun Jan 17, 2010 1:20 am
w = cube root of unity = 1
thus
a + b + c = x
a + b + c = y
a + b + c = z
x = y = z

therefore since x = y = z, we can replace y and z in the below equation with x
x^3 + y^3 + z^3 - 3 x y z
= x^3 + x^3 + x^3 - 3 x x x
= 3(x^3) - 3(x^3)
= 0

answer C
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