Question

if (x-1/x)=3 then find the value of (x³-1/x³)​

Answer 1

1. x - 1 / x = 3. On cubing both sides ; ( x - 1 / x ) = ( 3 )³ Using Identity :
2. ( a - b )³ = a³ - b³ - 3 ab ( a - b ) ⇒ x³ - 1 / x³ - 3 ( x - 1 / x ) = 27. ⇒ x³ - 1 / x³ - 3 ( 3 ) = 27. ⇒ x³ - 1 / x³ - 9 = 27. ⇒ x³ - 1 / x³ = 27 + 9. ⇒ x³ - 1 / x³ = 36.

Answer 2

Answer:

36

Step-by-step explanation :

x - 1 / x = 3

On cubing both sides ;

( x - 1 / x ) = ( 3 )³

Using Identity :

( a - b )³ = a³ - b³ - 3 ab ( a - b )

⇒ x³ - 1 / x³ - 3 ( x - 1 / x ) = 27

⇒ x³ - 1 / x³ - 3 ( 3 ) = 27

⇒ x³ - 1 / x³ - 9 = 27

⇒ x³ - 1 / x³ = 27 + 9

⇒ x³ - 1 / x³ = 36

Hence, the answer is 36

Step-by-step explanation:

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