SSC CHSL 15 Nov 2015 Shift 1 Paper

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Question : 142 of 199

Marks: +1, -0

If

a ^2 + a + 1 = 0

, then the value of

a^4 + a^2 + 1 = 0

is:

0
a + 1
1
$a^2$

Solution:

Given :

a ^2 + a + 1 = 0

Dividing both sides by 'a' , we get
⇒

a + 1 + 1/a = 0

⇒

a + 1/a = −1

Squaring both sides, we get :
⇒

(a + 1/a )^2 = (−1)^ 2

⇒

a^ 2 + 1/a ^2 + 1 2(a)(1/ a ) = 1

⇒

a ^2 + a ^2 = 1 − 2 = −1

⇒

a^4 + a^ 2 + 1 = 0

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