Harvard University Entrance Exam Question | Math Olympiad | Algebraic Expression | Pi Nerds

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  • เผยแพร่เมื่อ 12 ม.ค. 2025

ความคิดเห็น • 6

  • @Mike-H_UK
    @Mike-H_UK 18 วันที่ผ่านมา +1

    It is easier to look at each term in the sum for positive integer values of m & n. If m=1 then n=4 (maximum value and happens to be a valid integer solution in itself). Looking at the 2nd term, if n=1 then m=7 (maximum value that also happens to be a valid integer solution in itself). So we can conclude 1

  • @erenozturk5796
    @erenozturk5796 18 วันที่ผ่านมา +1

    wow 56/9 wow

  • @kablanetkablanet989
    @kablanetkablanet989 18 วันที่ผ่านมา +2

    It took me a second to figure out that N=4 and M=1 7+2=9

    • @tonylo9971
      @tonylo9971 18 วันที่ผ่านมา

      7 is a prime number and so m must be 1 or 7, otherwise 7/m is irrational. Then, it is easy to find n to be 4 or 1

    • @doyouknoworjustbelieve6694
      @doyouknoworjustbelieve6694 17 วันที่ผ่านมา

      @@tonylo9971
      (7/m)+(8/n) ‎ =  9. n,m are real positive numbers.
      This 2 variable equation has infinite solutions. You can substitute directly him the above equation, but for fun:
      (8/n) = 9- (7/m)
      (1/n) = (9- (7/m))/8
      n = 8/ (9- (7/m)), ………………… (1)
      on the condition 9-(7/m) > 0
      or m> 7/9
      Substitute in (1);
      m = 1
      n=8/2=4
      m=7
      n = 8/ (9-1) =1
      m = 100000000000000
      n less than 8/9