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      Question

      If a 2 ┬а+ b 2 ┬а= 89 and a

      2 ┬а- b 2 ┬а= 39, then find the value of a 3 ┬а- b 3 ┬а- 3ab, (a, b >0).
      A 267 Correct Answer Incorrect Answer
      B 271 Correct Answer Incorrect Answer
      C 283 Correct Answer Incorrect Answer
      D 252 Correct Answer Incorrect Answer

      Solution

      a 2 ┬а+ b 2 ┬а= 89 ........ (1)

      a 2 ┬а- b 2 ┬а= 39 ........ (2)

      From (1) and (2):

      a 2 ┬а= 64 => a = 8

      b 2 ┬а= 25 => b = 5

      Now,

      a 3 ┬а- b 3 ┬а- 3ab

      = 8 3 ┬а- 5 3 ┬а- 3 * 8 * 5 = 512 - 125 тАУ 120 = 267

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