Question 1012879
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S=small number; L=large number
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{{{S^2+L^2=106}}}
{{{L^2=106-S^2}}}
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{{{L+3S=24}}}
{{{L=24-3S}}}
{{{L^2=(24-3S)^2=9S^2-144S+576}}}
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{{{9S^2-144S+576=106-S^2}}}
{{{10S^2-144S+470=0}}}
{{{5S^2-72S+235=0}}}
{{{(5S-47)(S-5)=0}}}
{{{5S-47=0}}} {{{OR}}} {{{S-5=0}}}
{{{5S=47}}} {{{OR}}} {{{S=5}}}
{{{S=47/5}}} {{{OR}}} {{{S=5}}}
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ANSWER 1: The small number is 5.
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{{{L+3S=24}}}
{{{L+3(5)=24}}}
{{{L+15=24}}}
{{{L=9}}}
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ANSWER 2: The large number  is 9.
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CHECK
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{{{S^2+L^2=106}}}
{{{5^2+9^2=106}}}
{{{25+81=106}}}
{{{106=106}}}
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