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 60

Let b = 6, with a and c satisfying (E). If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$ax^2 + bx + c = 0$$, then $$\sum_{n=0}^{\infty}\left(\frac{1}{\alpha} + \frac{1}{\beta}\right)^n$$ is

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JEE (Advanced) 2011 Paper-1

Let b = 6, with a and c satisfying (E). If $$\alpha$$ and $$\beta$$ are the roots of the quadratic equation $$ax^2 + bx + c = 0$$, then $$\sum_{n=0}^{\infty}\left(\frac{1}{\alpha} + \frac{1}{\beta}\right)^n$$ is

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