A Nice Math Olympiad Algebra Problem

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  • Опубликовано: 5 ноя 2024

Комментарии • 11

  • @dibyamshumohapatra2890
    @dibyamshumohapatra2890 8 месяцев назад

    1/a+1/ab=1
    this means b+1/ab=1
    b+1=ab
    1=b(a-1)
    as a and b are naturals,the only possible pair of is b=1 and a-1=1 shich gives us the only solution i.e a=2 and b=1

  • @kolbasoed
    @kolbasoed 10 месяцев назад

    A=2, B=1
    1/2 + 1/2*1 = 1/2+1/2 = 2

  • @killmeister2271
    @killmeister2271 10 месяцев назад

    1/a+1/ab=1
    b/ab+1/ab=1
    b+1=ab
    b=2 & a=1

  • @nayR5
    @nayR5 10 месяцев назад

    (1/a)+(1/ab)=1
    (b/ab)+(1/ab)=1
    (1+b)/ab=1
    1+b=ab
    (1+b)/b=a
    (1/b)+1=a
    1+b=((1/b)+1)b
    (1+b)/b=(1/b)+b
    (1/b)+1=(1/b)+b
    *1=b*
    1+1=a
    *a=2*

  • @wes9627
    @wes9627 11 месяцев назад +1

    (1/a)(1 + 1/b) = 1
    (1 + b) = ab or a = (1 + b)/b
    b = 1 gives a = 2; b > 1 gives a = fraction; b < -1 gives a = fraction, so this is the only solution.

    • @AplusB7
      @AplusB7  11 месяцев назад

      Yes.... you are right.

    • @RealComplexity-math
      @RealComplexity-math 10 месяцев назад

      ​@@AplusB7No hes not, there are infinity solutions

  • @КатяРыбакова-ш2д
    @КатяРыбакова-ш2д 10 месяцев назад

    a=2, b=1 или a=1, b=-2.

  • @RealComplexity-math
    @RealComplexity-math 10 месяцев назад

    a = n
    and a is not equal to zero
    b = 1/(a-1)
    So there infinitely many solutions

  • @JSSTyger
    @JSSTyger 10 месяцев назад

    How about a = 2 and b = 1? I think thats the only solution.

    • @JSSTyger
      @JSSTyger 10 месяцев назад

      My reasoning is that 1/a must be greater than 1/ab to make this work. Also, 1/a must be 1/2 or greater. If a = 1, the equation fails. If a = 2 (the last possible option), b = 1.