Germany | A Nice Math Olympiad Problem | X = ? & Y = ?

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  • เผยแพร่เมื่อ 21 พ.ค. 2024
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ความคิดเห็น • 4

  • @swastik3423
    @swastik3423 28 วันที่ผ่านมา +1

    Sir, there is an easier way. Instead of taking x into quadratic form, we could make root(x)-root(y) by using a-b whole squared formula. After squaring root(x)+root(y) and getting the value of x+y, we see the squared expression and then subtract 4 times root (xy) to get x+y-2root(xy). This can then be brought into root(x)-root(y) form. Multiplying root(x)-root(y) with root(x)+root(y) will give us x-y. Ten after adding x+y and x-y equations, we can get x and y more easily....

    • @MasterTMathsClass
      @MasterTMathsClass  28 วันที่ผ่านมา +2

      Nice one, thank you 🎉

    • @ichdu6710
      @ichdu6710 8 วันที่ผ่านมา +1

      Method 3:
      This is a problem with 2 unknown variables in 2 equations.
      dividing √(xy) = 10 by √x leads to √y = 10/√x
      replacing √y in the first equation leads to √x + 10/√x = 10
      √x + 10/√x = 10 can be solved in following way:
      multiplying this with√x leads to x + 10 = 10√x. By squaring both sides you find
      x² - 80x + 100 = 0 with the solutions 40 + /- 10√15

    • @MasterTMathsClass
      @MasterTMathsClass  8 วันที่ผ่านมา

      @@ichdu6710 Nice one 🎉