Flos/Problems

Problems from Flos by Leonardo Fibonacci

Problem $1$

Find a rational number such that $5$ added to, or subtracted from, its square, is also a square.

Problem $2$

Solve the cubic:

$x^3 + 2 x^2 + 10 x = 20$

Problem $3$

$3$ men possess a pile of money, their shares being $\dfrac 1 2$, $\dfrac 1 3$ and $\dfrac 1 6$.

Each man takes some money from the pile until nothing is left.

The first man returns $\dfrac 1 2$ of what he took,

the second $\dfrac 1 3$

and the third $\dfrac 1 6$.

When the total so returned is divided equally among the men it is found that each then possess what he is entitled to.

How much money was in the original pile, and how much did each man take from the pile?