Initial program 35.7
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
Initial simplification35.7
\[\leadsto \sqrt[3]{\frac{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}{a \cdot 2}} + \sqrt[3]{\frac{\frac{-1}{2}}{a} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}\]
- Using strategy
rm Applied associate-*l/35.7
\[\leadsto \sqrt[3]{\frac{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}{a \cdot 2}} + \sqrt[3]{\color{blue}{\frac{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}{a}}}\]
Applied cbrt-div33.7
\[\leadsto \sqrt[3]{\frac{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g}{a \cdot 2}} + \color{blue}{\frac{\sqrt[3]{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}}{\sqrt[3]{a}}}\]
- Using strategy
rm Applied div-inv33.7
\[\leadsto \sqrt[3]{\color{blue}{\left(\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g\right) \cdot \frac{1}{a \cdot 2}}} + \frac{\sqrt[3]{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}}{\sqrt[3]{a}}\]
Applied cbrt-prod31.8
\[\leadsto \color{blue}{\sqrt[3]{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}} + \frac{\sqrt[3]{\frac{-1}{2} \cdot \left(g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}\right)}}{\sqrt[3]{a}}\]
- Using strategy
rm Applied add-cube-cbrt31.8
\[\leadsto \sqrt[3]{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\frac{-1}{2} \cdot \color{blue}{\left(\left(\sqrt[3]{g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}} \cdot \sqrt[3]{g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}\right) \cdot \sqrt[3]{g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}\right)}}}{\sqrt[3]{a}}\]
- Using strategy
rm Applied add-sqr-sqrt31.8
\[\leadsto \sqrt[3]{\sqrt{\left(g + h\right) \cdot \left(g - h\right)} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\frac{-1}{2} \cdot \left(\left(\sqrt[3]{g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}} \cdot \sqrt[3]{g + \color{blue}{\sqrt{\sqrt{\left(g + h\right) \cdot \left(g - h\right)}} \cdot \sqrt{\sqrt{\left(g + h\right) \cdot \left(g - h\right)}}}}\right) \cdot \sqrt[3]{g + \sqrt{\left(g + h\right) \cdot \left(g - h\right)}}\right)}}{\sqrt[3]{a}}\]
Final simplification31.8
\[\leadsto \sqrt[3]{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(\sqrt[3]{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} + g} \cdot \left(\sqrt[3]{\sqrt{\left(h + g\right) \cdot \left(g - h\right)} + g} \cdot \sqrt[3]{g + \sqrt{\sqrt{\left(h + g\right) \cdot \left(g - h\right)}} \cdot \sqrt{\sqrt{\left(h + g\right) \cdot \left(g - h\right)}}}\right)\right) \cdot \frac{-1}{2}}}{\sqrt[3]{a}}\]
