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      Question

      The sum of two numbers is 17 while the sum of their

      squares is 157. Find the sum of the cubes of those two numbers.
      A 3791 Correct Answer Incorrect Answer
      B 3094 Correct Answer Incorrect Answer
      C 1491 Correct Answer Incorrect Answer
      D 1547 Correct Answer Incorrect Answer

      Solution

      Let the number is a and b. ATQ- a+b =17 a2+b2 =157 (a+b)2 = a2+b2 +2ab. 17×17 =157+2ab 2ab =289-157=132. ab =66 (11,6) is the prime factor of 66. So, a=11, and b =6 Now, a3+b3=1331+216=1547.

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