Initial program 35.4
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
- Using strategy
rm Applied add-cube-cbrt35.5
\[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \color{blue}{\left(\left(\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}}\right) \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}}\right)}} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Applied simplify35.5
\[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\color{blue}{\left(\sqrt[3]{\sqrt{\left(g - h\right) \cdot \left(g + h\right)} - g} \cdot \sqrt[3]{\sqrt{\left(g - h\right) \cdot \left(g + h\right)} - g}\right)} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Applied simplify35.5
\[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(\sqrt[3]{\sqrt{\left(g - h\right) \cdot \left(g + h\right)} - g} \cdot \sqrt[3]{\sqrt{\left(g - h\right) \cdot \left(g + h\right)} - g}\right) \cdot \color{blue}{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Taylor expanded around -inf 35.5
\[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(\sqrt[3]{\sqrt{\left(g - h\right) \cdot \left(g + h\right)} - g} \cdot \sqrt[3]{\sqrt{\left(g - h\right) \cdot \left(g + h\right)} - g}\right) \cdot \sqrt[3]{\color{blue}{-1 \cdot g} - g}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Applied simplify35.5
\[\leadsto \color{blue}{\sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(h + g\right) \cdot \left(g - h\right)}}{a \cdot 2}} + \sqrt[3]{\sqrt[3]{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} - g} \cdot \left(\sqrt[3]{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} - g} \cdot \left(\sqrt[3]{\left(-g\right) + \left(-g\right)} \cdot \frac{1}{a \cdot 2}\right)\right)}}\]
Applied simplify35.5
\[\leadsto \sqrt[3]{\frac{\left(-g\right) - \sqrt{\left(h + g\right) \cdot \left(g - h\right)}}{a \cdot 2}} + \color{blue}{\sqrt[3]{\left(\sqrt[3]{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g} \cdot \left(\sqrt[3]{-\left(g + g\right)} \cdot \frac{1}{2 \cdot a}\right)\right) \cdot \sqrt[3]{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}}}\]
