Question 1156496

The sum of a number and its reciprocal is 37/6. Find the number.
<pre>Let the numbers be N
Then we get: {{{matrix(1,3, N + 1/N, "=", 37/6)}}}
{{{matrix(1,3, 6N^2 + 6, "=", 37N)}}} ------ Multiplying by LCD, 6N
{{{matrix(2,3, 6N^2 - 37N + 6, "=", 0, 6N^2 - 36N - N + 6, "=", 0)}}}
6N(N - 6) - 1(N - 6) = 0
(6N - 1)(N - 6) = 0
6N - 1 = 0           or           N - 6 = 0
{{{highlight_green(matrix(1,7, N, or, number, "=", 1/6, or, 6))}}}