Question

Which of the following is the value of (x+ 1/x)2?
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Answer 1

Answer:-

To Find:-

Value of (x + x⁻¹)².

Procedure:-

We know,

(a + b)² = a² + b² + 2ab

∴ (x + 1/x)²

= (x)² + 2(x)(1/x) + (1/x)²

= x² + 1/x² + 2

(= x² + x⁻² + 2)

∴ (c) ☑ is the correct expanded form of (x + 1/x)².

Answer 2

The value of (x + 1/x)² will be x² + 1/x² + 2 (option 3).

Given,

(x + 1/x)²

To find,

The value of (x + 1/x)².

Solution,

The value of (x + 1/x)² will be x² + 1/x² + 2.

We can easily solve this problem by following the given steps.

We can solve (x + 1/x)² using the identity (a+b)².

We know that (a+b)² is (a² + b² + 2ab).

In this case, (x) will be in the place of (a) and (1/x) will be in the place of (b).

Now, using the identity,

(x + 1/x)² = (x)² + (1/x)² + 2 × x × (1/x)

(x + 1/x)² = x² + 1/x² + 2

[The square of 1 is 1. So, (1/x)² has been written as 1/x². In 2 × x × (1/x), x has been divided by the x from (1/x).]

Hence, the correct answer is x² + 1/x² + 2.