Question

Please answer this question.

Answer 1

Answer:

(NOTE: WE TOOK X INSTEAD OF A)

x⁴ + 1/x⁴ = 119

=> x⁴ + 1/x⁴ + 2 = 121

=> (x² + 1/x²) ² = 11²

=> x² + 1/x² = 11    ,  ignore the negative value as LHS is +ve.

=> x² + 1/x² - 2 = 9

=> (x - 1/x)² = 3²

=> x - 1/x = +3 or -3

=> (x - 1/x)³ = x³ - 1/x³ - 3 x * 1/x * (x - 1/x)

     (+ 3) ³ = x³ - 1/x³ - 3 ( + 3)

Answer:      x³ - 1/x³ = 3³ + 9 or -30 - 9 = + 36 

Answer 2

Answer:

36

Step-by-step explanation:

⇒ a^4 + 1 / a^4 = 119

  Adding 2 on both sides

⇒ a^4 + 1 / a^4 + 2 = 119 + 2

⇒ a⁴ + 1 / a⁴ + 2( a² * 1 / a² ) = 121

  Using a⁴ + b⁴ + 2a²b² = ( a² + b² )²

⇒ ( a² + 1 / a² )² = 121

⇒ a² + 1 / a² = 11

    Adding - 2 on both sides:

⇒ a² + 1 / a² - 2 = 11 - 2

⇒ a² + 1 / a² - 2( a * 1 / a) = 9

⇒ ( a - 1 / a )² = 9

⇒ ( a - 1 / a ) = 3  

  Cubing both sides:

⇒ ( a - 1 / a )³ = 3³

⇒ a³ - 1 / a³ - 3( a*1/a )( a - 1 / a ) = 27

⇒ a³ - 1 / a³ - 3( 1 )( 3 ) = 27

⇒ a³ - 1 / a³ - 9 = 27

⇒ a³ - 1 / a³ = 27 + 9

⇒ a³ - 1 / a³ = 36