MathematicsIf a+b=12 and ab=27, find the value of a3+b3.

If a+b=12 and ab=27, find the value of a3+b3.


  1. A
    752
  2. B
    756
  3. C
    753
  4. D
    754 

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    Solution:

    It is given that a+b=12 and ab=27
    We have to find the value of a3+b3.
    We know the algebraic identity, a+b3=a3+b3+3aba+b .
    Put the value of a+b=12 in above identity, we get,
    123=a3+b3+3ab12 (12)3=a3+b3+3(27)(12)
    12×12×12=a3+b3+3(27)(12)
    1728=a3+b3+972
    a3+b3=1728-972
    a3+b3=756
    Therefore, option 2 is  correct.
     
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