Question

the sum of a number and its reciprocal is 13/6. find the numbers.

Answer 1

Let the number = x
\[x+\frac{1}{x}=\frac{13}{6}\]
\[\frac{x ^{2}+1}{x}=\frac{13}{6}\]
\[x ^{2}+1=\frac{13}{6}x\]
\[x ^{2}-\frac{13}{6}+1=0\ ................(1)\]
Now solve quadratic (1) using the formula that will solve any quadratic.