Question 1066053

Evaluate a^3 + 1/a^3 if a + 1/a = 6.
<pre>{{{a^3 + 1/a^3}}}         			{{{a + 1/a = 6}}}

{{{(a + 1/a)^2 = 6^2}}} ------ Squaring the equation: {{{a + 1/a = 6}}}
{{{a^2 + 2 + 1/a^2 = 36}}}
{{{a^2 + 1/a^2 = 34}}}

{{{a^3 + 1/a^3}}}
{{{(a + 1/a)(a^2 - 1 + 1/a^2)}}} ------ Factoring {{{a^3 + 1/a^3}}}
{{{(a + 1/a)(a^2 + 1/a^2 - 1)}}}

6(34 - 1) ------- Substituting {{{matrix(1,7, 6, for, a + 1/a, and, 34, for, a^2 + 1/a^2)}}}
{{{highlight_green(matrix(1,5, a^3 + 1/a^3, "=", 6(33), "=", 198))}}}</pre>