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SSC CHSL 2019 PYQ — Question 54

SSC CHSL - 9th July 2019 - Shift 1 • Quantitative Aptitude • Q54

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If x = 2 + √5 then the value of x3 + 1/x3 is:

Show answer & explanation

Correct answer: D

Explanation

Correct Answer is option 4 i.e. 34√5

Understanding

Application

If

x + 1/x = a

Then

x3 + 1/x3 = a3 – 3a

Given:

x = 2 + √5

Then,

1/x = √5 – 2

Now

x + 1/x = 2 + √5 + √5 – 2 

 x + 1/x = 2√5

So

x3 + 1/x3 = (2√5)3 – 3 × (2√5) = 40√5 – 6√5

= 34√5