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Evaluate the Following Using Identities: (2x+ 1/X)^2 - Mathematics

Evaluate the following using identities:

`(2x+ 1/x)^2`

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Solution

In the given problem, we have to evaluate expressions by using identities.

Given `[2x - 1/x]^2`

We shall use the identity `(a - b)^2 = a^2 - 2ab + b^2`

Here a = 2x

`b = 1/x`

By applying identity we get 

`[2x - 1/x]^2 = (2x)^2 + (1/x)^2 - 2 xx 2 xx x xx 1/x`

`= (2x xx 2x) + (1/x xx 1/x) - 2 xx 2 xx x xx 1/x` 

` = 4x^2 + 1/x^2 - 4`

Hence the value of `[2x - 1/x]^2 is [4x^2 + 1/x^2 - 4]`

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.1 | Q 1.1 | Page 6
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