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SSC CPO Tier 1 Exam 9 Dec 2025 Shift 2

Section: Quantitative Aptitude

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Question : 104 of 200

Marks: +1, -0

Given:

\rm x+\frac{1}{x}=2

, find the value of

\rm x^6+\frac{1}{x^6}-3\left(x^3-\frac{1}{x^3}\right)+5\left(x^2+\frac{1}{x^2}\right)

2
4
12
8

Solution:

Concept:

If

x + \frac{1}{x} = 2

, then solving gives

x = 1

. This is because the equation simplifies to

(x-1)^2 = 0

.

Explanation:

Given

x + \frac{1}{x} = 2

, we get

x = 1

.

Now compute each term:

x^6 + \frac{1}{x^6} = 1 + 1 = 2

,

x^3 - \frac{1}{x^3} = 1 - 1 = 0

,

x^2 + \frac{1}{x^2} = 1 + 1 = 2

.

Plug these into the given expression:

2 - 3(0) + 5(2) = 2 + 10 = 12

.

Answer:

12 (Option C)

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