Question

Plz...very important ​

Answer 1

Answer:

4266

Step-by-step explanation:

Given---> x + 1 / x = 9 and x - 1/x = 6

To find ---> x⁴ - 1 / x⁴ = ?

Solution---> ATQ,

x + 1 /x = 9

Squaring both sides, we get,

=> ( x + 1 / x )² = ( 9 )²

We have an identity as follows,

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

=> x² + 1 / x² + 2 x ( 1 / x ) = 81

=> x² + 1 / x² + 2 = 81

=> x² + 1 / x² = 81 - 2

=> x² + 1 / x² = 79

Now,

x⁴ - 1 / x⁴ = ( x² )² - ( 1 / x² )²

We have a formula, a² - b² = ( a + b ) ( a - b ), applying it here , we get,

= ( x² + 1 / x² ) ( x² - 1 / x² )

= ( x² + 1 / x² ) { ( x )² - ( 1 / x )² }

= ( x² + 1 / x² ) ( x + 1 / x ) ( x - 1 / x )

= ( 79 ) ( 9 ) ( 6 )

= 79 × 54

= 4266

Answer 2

Answer:

Step-by-step explanation:

Given

x + 1 / x = 9

x - 1/x = 6

x⁴ - 1 / x⁴ = ?

Solution

x + 1 /x = 9

Squaring both sides, we get,

=> ( x + 1 / x )² = ( 9 )²

We have an identity as follows,

( a + b )² = a² + b² + 2ab,

=> x² + 1 / x² + 2 x ( 1 / x ) = 81

=> x² + 1 / x² + 2 = 81

=> x² + 1 / x² = 81 - 2

=> x² + 1 / x² = 79

x⁴ - 1 / x⁴ = ( x² )² - ( 1 / x² )²

We have a formula,

a² - b² = ( a + b ) ( a - b ),

= ( x² + 1 / x² ) ( x² - 1 / x² )

= ( x² + 1 / x² ) { ( x )² - ( 1 / x )² }

= ( x² + 1 / x² ) ( x + 1 / x ) ( x - 1 / x )

= ( 79 ) ( 9 ) ( 6 )

= 79 × 54

= 4266