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If $x + 1 x = 5,$ then $x 2 + 1 x 2 = ?$

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answer is C.

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Detailed Solution

Given,

x + 1 x = 5

To find the value of

x 2 + 1 x 2

We know that,

(x + y) 2 = x 2 + y 2 + 2 x y

Therefore, we have,

⇒ x + 1 x 2 = x 2 + 1 x 2 + 2 (x) 1 x

⇒ x + 1 x 2 = x 2 + 1 x 2 + 2

Put

x + 1 x = 5

. We get,

⇒ 52 = x 2 + 1 x 2 + 2

⇒ 25 = x 2 + 1 x 2 + 2

⇒ 25 − 2 = x 2 + 1 x 2

⇒ x 2 + 1 x 2 = 23

Hence, the value of

x 2 + 1 x 2 = 23

.
Therefore, option 3 is correct.

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