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Suppose that x and y are positive integers such that x^2 * y^3=46656. What is the sum of all possible values of x?

Suppose that x and y are positive integers such that x^2 * y^3=46656. What is the sum of all possible values of x?
asked 55.5k views
5 votes
Suppose that x and y are positive integers such that x^2 * y^3=46656. What is the sum of all possible values of x?

asked
User Zana
by
7.6k points

1 Answer

7 votes

Answer:

252

Explanation:

  • x² * y³=46656

Prime factors of 46656:

  • 46656 = 2⁶3⁶

Possible values of x:

  • (2*3)³= 216
  • 3³ = 27
  • 2³ = 8
  • 1

Sum of them:

  • 216 + 27 + 8 + 1 = 252
answered
User Inon Stelman
by
8.2k points
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