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XAT 2019 — QA & DI Question 17

Remainder of a to the power n, divided by b.Easy

If x2 + x + 1 = 0, then x2018 + x2019 equals which of the following: 

Answer & solution

  • -x

  • B

    x

  • C

    None of the others

  • D

    x - 1

  • E

    x + 1

Solution

x2 + x + 1 = 0   …(1)

⇒ x2 = - x – 1   …(2)

Multiplying x in (2)
⇒ x3 = - x2 – x

⇒ x3 = 1   …(3) [From (1)]

Now, 

x2018 + x2019 = x2018(1 + x)

= x2018 × -x2

= -x2020

= - (x3)673 × x

 = - 1 × x

= - x

∴ x2018 + x2019 = - x

Hence, option (a).

XAT 2019 QA & DI Q17: If x 2 + x + 1 = 0, then x 2018 + x 2019 equals which of the following: — Solution | TheCATExam