Test Index

UPSC NDA 2 2021 Mathematics Solved Paper

© examsnet.com

Question : 1 of 120

Marks: +1, -0

If

x^{2} + x + 1 = 0

, then what is the value of

x^{199} + x^{200} + x^{201}

?

$-1$
0
1
3

Solution:

Concept:

Factor the expression to use the given equation

x^{2} + x + 1 = 0

.

Explanation:

We are given

x^{2} + x + 1 = 0

.

We need

x^{199} + x^{200} + x^{201}

.

Factor out the common term

x^{199}

:

x^{199}(1 + x + x^{2})

.

From the given equation,

1 + x + x^{2} = 0

.

Thus the expression becomes

x^{199} \times 0 = 0

.

So the value simplifies to zero.

Answer:

0

© examsnet.com

Go to Question:

Next Question