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SSC CGL Tier I 12 Sep 2025 Shift 2 Paper

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Question : 71 of 100

Marks: +1, -0

If x = √7, determine the value of x + (1)/(x).

$\frac{8√(7)}{7}$
$\frac{7√(7)}{8}$
$\frac{7√(7)}{9}$
$\frac{9√(7)}{7}$

Solution:

Concept:

Rationalize the denominator of

1/x

and then add to

x

.

Explanation:

Given

x = \sqrt{7}

.

First, find

1/x = 1/\sqrt{7}

. Multiply numerator and denominator by

\sqrt{7}

to get

\sqrt{7}/7

.

Now,

x + 1/x = \sqrt{7} + \sqrt{7}/7

.

Write

\sqrt{7}

as

7\sqrt{7}/7

to combine terms:

7\sqrt{7}/7 + \sqrt{7}/7 = (7\sqrt{7} + \sqrt{7})/7 = 8\sqrt{7}/7

.

Answer:

A.

\frac{8\sqrt{7}}{7}

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