Instructions

Let a, b and c be three real numbers satisfying
$$\begin{bmatrix}a & b & c \end{bmatrix}\begin{bmatrix}1 & 9 & 7 \\8 & 2 & 7 \\7 & 3 & 7\end{bmatrix} = \begin{bmatrix}0 & 0 & 0 \end{bmatrix} .............(E)$$

Question 59

Let $$\omega$$ be a solution of $$x^3 - 1 = 0$$ with $$Im(\omega) > 0$$. If a = 2 with b and c satisfying (E), then the value of $$\frac{3}{\omega^a} + \frac{1}{\omega^b} + \frac{3}{\omega^c}$$ is equal to

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JEE (Advanced) 2011 Paper-1

Let $$\omega$$ be a solution of $$x^3 - 1 = 0$$ with $$Im(\omega) > 0$$. If a = 2 with b and c satisfying (E), then the value of $$\frac{3}{\omega^a} + \frac{1}{\omega^b} + \frac{3}{\omega^c}$$ is equal to

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