Question 1082554
{{{x-1/x =4}}}, find the value of {{{x^3-1/x^3}}} and {{{x^4+1/x^4}}}
<pre><b>
{{{x-1/x =4}}}

Square both sides:

{{{x^2-2(x)(1/x)+1/x^2=16}}}

{{{x^2-2+1/x^2 =16}}}

{{{x^2+1/x^2 =18}}}   <-- the answer to 1st expression

Square both sides again

{{{x^4+2x^2(1/x^2)+1/x^4=324}}}

{{{x^4+2+1/x^4 =324}}}

{{{x^4+1/x^4 =322}}}  <-- the answer to 3rd expression

For the 2nd expression, take the two equations:

{{{x-1/x =4}}} and {{{x^2+1/x^2 =18}}}

Multiply equals by equals:

{{{(x-1/x)(x^2+1/x^2) = (4)(18)}}}

{{{x^3+x(1/x^2)-(1/x)(x^2)-1/x^3=72}}}

{{{x^3+1/x-x-1/x^3=72}}}

{{{x^3-1/x^3=72+x-1/x}}}

{{{x^3-1/x^3=72+(x-1/x)}}}, and since {{{x-1/x =4}}},

{{{x^3-1/x^3=72+4}}}

{{{x^3-1/x^3=76}}} <-- answer to 2nd expression

Edwin</pre></b>