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      Question

      If, ( a + b = 12 ) and ( a² + b² = 80 ), then find the

      value of (a³ + b³).  
      A 560 Correct Answer Incorrect Answer
      B 568 Correct Answer Incorrect Answer
      C 576 Correct Answer Incorrect Answer
      D 584 Correct Answer Incorrect Answer

      Solution

      ( a + b = 12 )
      ( (a + b) ² = 12² )
      ( a² + b² + 2ab = 144 )
      ( 80 + 2ab = 144 )
      ( 2ab = 64 ab = 32 )
      (a³ + b³ = (a + b)(a² + b² - ab) ) = 12 (80 - 32) = 12 * 48 = 576 )

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