Question

find the square root of the following x power 4 + 1/xpower4+2​

Answer 1

Answer:

( x² + 1 / x² )

Step-by-step explanation:

To find----> Square root of x⁴ + 1 / x⁴ + 2 .

Solution----> ATQ,

x⁴ + 1 / x⁴ + 2

Multiplying and dividing by x² in third term , we get,

= ( x² )² + ( 1 / x² )² + 2 ( x² ) ( 1 / x² )

We have an identity ,as follows

a² + b² + 2ab = ( a + b )² , applying it , we get,

= { x² + ( 1 / x² ) }²

Now

Square root of ( x⁴ + 1 / x⁴ + 2 ) = √(x⁴ + 1/x⁴ + 2 )

= √{ x² + ( 1 / x² ) }²

= ( x² + 1 / x² )

Additional identities ---->

1) ( a - b )² = a² + b² - 2ab

2) ( a² - b² ) = ( a + b ) ( a - b )

3) ( a³ + b³ ) = ( a + b ) ( a² + b² - ab )

4) ( a³ - b³ ) = ( a - b ) ( a² + b² + ab )

5) ( a + b )³ = a³ + b³ + 3ab ( a + b )

6) ( a - b )³ = a³ - b³ - 3ab ( a - b )