Question

How can we find the absolute minimum value of function x^4-x^2+2x+5?

Answer 1

\left[x _{1}\right] = \left[ \frac{\sqrt{\left( \frac{2}{3}+\frac{61\,\sqrt[3]{2}}{3\,\sqrt[3]{\left( 466+\left( 36\,i \right) \,\sqrt{533}\right) }}+\frac{\sqrt[3]{\left( 466+\left( 36\,i \right) \,\sqrt{533}\right) }}{3\,\sqrt[3]{2}}\right) }}{2}+\frac{ - \sqrt{\left( \frac{4}{3}+\frac{\left( -61\right) \,\sqrt[3]{2}}{3\,\sqrt[3]{\left( 466+\left( 36\,i \right) \,\sqrt{533}\right) }}+\frac{ - \sqrt[3]{\left( 466+\left( 36\,i \right) \,\sqrt{533}\right) }}{3\,\sqrt[3]{2}}+\frac{-4}{\sqrt{\left( \frac{2}{3}+\frac{61\,\sqrt[3]{2}}{3\,\sqrt[3]{\left( 466+\left( 36\,i \right) \,\sqrt{533}\right) }}+\frac{\sqrt[3]{\left( 466+\left( 36\,i \right) \,\sqrt{533}\right) }}{3\,\sqrt[3]{2}}\right) }}\right) }}{2}\right][x​1​​]=​⎣​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎢​⎡​​​2​​√​(​3​​2​​+​3​3​​√​(466+(36i)√​533​​​)​​​​​61​3​​√​2​​​​​+​3​3​​√​2​​​​​​3​​√​(466+(36i)√​533​​​)​​​​​)​​​​​+​2​​−​⎷​​​​​​​​​​​​⎝​⎜​⎜​⎜​⎜​⎛​​​3​​4​​+​3​3​​√​(466+(36i)√​533​​​)​​​​​(−61)​3​​√​2​​​​​+​3​3​​√​2​​​​​−​3​​√​(466+(36i)√​533​​​)​​​​​+​√​(​3​​2​​+​3​3​​√​(466+(36i)√​533​​​)​​​​​61​3​​√​2​​​​​+​3​3​​√​2​​​​​​3​​√​(466+(36i)√​533​​​)​​​​​)​​​​​−4​​​⎠​⎟​⎟​⎟​⎟​⎞​​​​​​​​⎦​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎥​⎤​​

totally answer. Algebra functional value