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SSC CGL Tier I 13 Sep 2025 Shift 2 Paper

Question : 75 of 100

Marks: +1, -0

Given, x + 1/

x = 6

x^{2} + 1/x^{2}

Solution:

Concept:

Use the algebraic identity

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

to relate the given sum to the required sum of squares.

Explanation:

We are given

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

Square both sides:

(x + \frac{1}{x})^{2} = 6^{2} = 36

Expand the left side:

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

So,

x^{2} + \frac{1}{x^{2}} + 2 = 36

Subtract 2 from both sides:

x^{2} + \frac{1}{x^{2}} = 36 - 2 = 34

Thus, the required value is 34.

Answer:

34, which corresponds to option C.

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