Question

In 1535 , the mathematician Antonio Fior challenged his rival Niccolo Tartaglia to solve this problem: A tree stands 12 braccia high; it is broken into two parts at such a point that the height of the part left standing is the cube root of the length of the part cut away. What is the height of the part left standing? Show that this is equivalent to solving $x^{3}+x=12$ and find the height to three decimal places. Tartaglia, who had discovered the secret of the cubic equation, was able to determine the exact answer: $$ x=(\sqrt[3]{\sqrt{2,919}+54}-\sqrt[3]{\sqrt{2,919}-54}) / \sqrt[3]{9} $$

          In 1535 , the mathematician Antonio Fior challenged his rival Niccolo Tartaglia to solve this problem: A tree stands 12 braccia high; it is broken into two parts at such a point that the height of the part left standing is the cube root of the length of the part cut away. What is the height of the part left standing? Show that this is equivalent to solving $x^{3}+x=12$ and find the height to three decimal places. Tartaglia, who had discovered the secret of the cubic equation, was able to determine the exact answer:
$$
x=(\sqrt[3]{\sqrt{2,919}+54}-\sqrt[3]{\sqrt{2,919}-54}) / \sqrt[3]{9}
$$

Added by Adri-N C.

Question

Please give Ace some feedback