The value of where satisfies the equation , is

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Solution

Q.
The value of $\sum_{r = 1}^{5} {(x^{r} + \frac{1}{x^{r}})}^{2},$ where $x$ satisfies the equation $x^{2} + x + 1 = 0$ , is

1 5

2 6

3 7

4 8

Ans.
(4)

$x^{2} + x + 1 = 0 \Rightarrow x + \frac{1}{x} = - 1$

$∴$ $\sum_{r = 1}^{5} {(x^{r} + \frac{1}{x^{r}})}^{2} = 8$

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