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UPD ON 2024-06-21-19:59:37:
新增内容：更加有趣的（一元四次方程求根公式）
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有趣的东西
更加有趣的（一元四次方程求根公式）：
一元四次方程：
ax4+bx3+cx2+dx+e=0ax^4+bx^3+cx^2+dx+e=0ax4+bx3+cx2+dx+e=0
求根公式：
x={x1=b4a+12b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)−12b22a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23−2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)+−b3+4bc−8a2d4a3b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)x2=b4a+12b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)+12b22a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23−2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)+−b3+4bc−8a2d4a3b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)x3=b4a−12b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)−12b22a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23−2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)+−b3+4bc−8a2d4a3b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)x4=b4a−12b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)+12b22a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23−2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)+−b3+4bc−8a2d4a3b24a2−4c3a+23(c2−3bd+12ae)3a2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)23+2c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)233(2a3)x=
\begin{cases}
x_1=\frac{b}{4a}+\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}
-
\frac{1}{2}\sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}+\frac{-b^3+4bc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}}}
\\
x_2=\frac{b}{4a}+\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}
+
\frac{1}{2}\sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}+\frac{-b^3+4bc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}}}
\\ x_3=\frac{b}{4a} -
\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}
-
\frac{1}{2}\sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}+\frac{-b^3+4bc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}}}
\\
x_4=\frac{b}{4a}-\frac{1}{2}\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}
+
\frac{1}{2}\sqrt{\frac{b^2}{2a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}-\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}+\frac{-b^3+4bc-8a^2d}{4a^3\sqrt{\frac{b^2}{4a^2}-\frac{4c}{3a}+\frac{\sqrt[3]{2}(c^2-3bd+12ae)}{3a\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}+\frac{\sqrt[3]{2c^3-9bcd+27ad^2+27b^2e-72ace+\sqrt{-4(c^2-3bd+12ae)^3+(2c^3-9bcd+27ad^2+27b^2e-72ace)^2}}}{3(\sqrt[3]{2a})}}}}
\end{cases} x=⎩⎨⎧ x1 =4ab +21 4a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) +3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 −21 2a2b2 −3a4c
+3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) −3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 +4a34a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) +3(32a
)32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 −b3+4bc−8a2d x2 =4ab +21 4a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) +3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 +21 2a2b2
−3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) −3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 +4a34a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae)
+3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 −b3+4bc−8a2d x3 =4ab −21 4a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) +3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2
−21 2a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) −3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 +4a34a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32
(c2−3bd+12ae) +3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 −b3+4bc−8a2d x4 =4ab −21 4a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) +3(32a
)32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 +21 2a2b2 −3a4c +3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) −3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 +4a34a2b2 −3a4c
+3a32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 32 (c2−3bd+12ae) +3(32a )32c3−9bcd+27ad2+27b2e−72ace+−4(c2−3bd+12ae)3+(2c3−9bcd+27ad2+27b2e−72ace)2 −b3+4bc−8a2d
鬼知道我打了多久……
