Question 1086530
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<pre>
1.  From  {{{(x+(1/x))^2}}} = 7  you have  {{{x+(1/x)}}} = {{{sqrt(7)}}}.


2.  It implies 

    {{{(sqrt(7))^3}}} = {{{7*sqrt(7)}}} = {{{(x + 1/x)^3}}} = {{{x^3 + 3x^2*(1/x)}}} + {{{3x*(1/x)^2 + (1/x)^3}}} = {{{x^3 + 1/x^3}}} + {{{3x + 3*(1/x)}}} = {{{(x^3 + 1/x^3)}}} + {{{3*(x + 1/x)}}}.


    Now replace in the last term  {{{x + 1/x}}}  by  {{{sqrt(7)}}}  (based on n.1),  and you will get

    {{{7*sqrt(7)}}} = {{{(x^3 + 1/x^3)}}} + {{{3*sqrt(7)}}},   or


    {{{x^3 + 1/x^3}}} = {{{4*sqrt(7)}}}.
</pre>

<U>Answer</U>.  &nbsp;&nbsp;{{{x^3 + 1/x^3}}} = {{{4*sqrt(7)}}}.



Solved.