Question

If x + (1/x) = √3, then find the value of x³ + (1/x)³​

Answer 1

: 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.

Answer 2

Answer:

x³ + (1/x)³  = 0

Step-by-step explanation:

Given :- x + (1/x) = √3

To Find :- Value of x³ + (1/x)³​

Solution :-

We know that,

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

                       ( a + b )² = a² + b² + 2ab

                    ⇒ a² + b² =  (a+b)² - 2ab

Here, x + (1/x) = √3

x³ + (1/x)³ = (x + (1/x) )( x² - x(1/x) + (1/x)² )

                = √3(x² - 1 + (1/x)² )

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

                = √3( (√3)² - 2 - 1 )

                = √3( 3 - 3 )

                = √3 × 0

                = 0

Therefore,  x³ + (1/x)³  = 0.

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