Question 1209837
<br>
{{{a+b=14}}}<br>
{{{(a+b)^2=a^2+2ab+b^2=196}}} --> {{{a^2+b^2=196-2ab}}}<br>
{{{(a+b)^3=a^3+3a^2b+3ab^2+b^3=2744}}} --> {{{a^3+b^3=2744-3ab(a+b)=2744-42ab}}}<br>
{{{a^3+b^3=812+a^2+b^2}}}
{{{2744-42ab=812+196-2ab}}}
{{{1736=40ab}}}
{{{ab=217/5}}}<br>
{{{a(14-a)=217/5}}}
{{{14a-a^2=217/5}}}
{{{a^2-14a+217/5=0}}}<br>
Use the quadratic formula....<br>
{{{a=7+2sqrt(35)/5}}} or {{{a=7-2sqrt(35)/5}}}<br>
ANSWER: The two numbers a and b are, in either order, {{{7+2sqrt(35)/5}}} and {{{7-2sqrt(35)/5}}}<br>