Question

If 9x^2+1/9x^2=23 find 3x+1/3x​

Answer 1

Answer:

± 5

Step-by-step explanation:

Given---> 9x² + ( 1 / 9x² ) = 23

To find---> 3x + ( 1 / 3x )

Solution---> We have an identity , as follows,

( a + b )² = a² + b² + 2ab

Now , applying it ,

( 3x + 1 / 3x )² = ( 3x )² + ( 1 / 3x )² + 2 ( 3x ) ( 1 / 3x )

= 9x² + 1 / 9x² + 2

= { 9x² + ( 1 / 9x² ) } + 2

Putting 9x² + 1 / 9x² = 23 , we get,

= ( 23 ) + 2

( 3x + 1 / 3x )² = 25

3x + 1 / 3x = ± 5

Additional information --->

1) ( a - b )² = a² + b² - 2ab

2) ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

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

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

5) a² - b² = ( a + b ) ( a - b )

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

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

Answer 2

Answer:

( a + b )² = a² + b² + 2ab

( 3x + 1 / 3x )² = ( 3x )² + ( 1 / 3x )² + 2 ( 3x ) ( 1 / 3x )

= 9x² + 1 / 9x² + 2

= { 9x² + ( 1 / 9x² ) } + 2

Putting 9x² + 1 / 9x² = 23 , we get,

= ( 23 ) + 2

( 3x + 1 / 3x )² = 25

3x + 1 / 3x = ± 5