Question 1118033
If sqrt(5)= 2+ 1/a, show that a= 4+1/a
<pre>{{{matrix(1,3, sqrt(5), "=", 2 + 1/a)}}}
{{{matrix(1,3, a * sqrt(5), "=", 2a + 1)}}} --------- Multiplying by LCD, a
{{{matrix(1,3, 5a^2, "=", 4a^2 + 4a + 1 )}}} ---- Squaring each side
{{{matrix(1,3, a^2, "=", 4a + 1)}}}
{{{highlight_green(matrix(1,3, a, "=", 4 + 1/a))}}} ------- Dividing by a</pre><pre>OR
<pre>{{{matrix(1,3, sqrt(5), "=", 2 + 1/a)}}}
{{{matrix(1,3, 5, "=", 4 + 4/a + 1/a^2)}}} ---- Squaring each side
{{{matrix(1,3, 1, "=", 4/a + 1/a^2)}}}
{{{highlight_green(matrix(1,3, a, "=", 4 + 1/a))}}} ------- Multiplying by a</pre>