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Math Quiz
Find the pair of three natural numbers which have an equal sum and product.
Hint: Let [tex]1\ \textless \ a

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Math Quiz
Find the pair of three natural numbers which have an equal sum and product.
Hint: Let [tex]1\ \textless \ a\ \textless \ b\ \textless \ c[/tex], so that [tex]0\ \textless \ \dfrac{1}{c} \ \textless \ \dfrac{1}{b} \ \textless \ \dfrac{1}{a} \ \textless \ 1[/tex].

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Passage: A number which can be written in
the form of where p, q E

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2 thoughts on “Math Quiz<br /> Find the pair of three natural numbers which have an equal sum and product.<br /> Hint: Let [tex]1\ \textless \ a”

  1. Given condition is [tex]abc=a+b+c[/tex]. …[I]

    Let [tex]1\leq a\leq b\leq c[/tex]. …[II]

    Divide [I] by [tex]c[/tex]

    [tex]ab=\dfrac{a}{c} +\dfrac{b}{c} +1[/tex]

    And by [II], [tex]0< \dfrac{a}{c} \leq \dfrac{b}{c} \leq \dfrac{c}{c} =1[/tex], we have [tex]1<ab<3[/tex]. Hence [tex]ab=2[/tex].

    The first two numbers are [tex]\boxed{a=1, b=2}[/tex].

    Now, all we have is an equation.

    [tex]abc=a+b+c[/tex]

    [tex]\rightarrow 2c=1+2+c[/tex]

    [tex]\therefore \boxed{c=3}[/tex]

    The pair of three numbers is [tex](a,b,c)=(1,2,3)[/tex].

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