展开 ((sqrt(E)-sqrt(E-V))^4)/(V^2)

解答

展开

\frac{( E - E - V ) ^{4}}{V ^{2}}

\frac{8 E ^{2}}{V ^{2}} - \frac{8 E}{V} - \frac{4 E ^{\frac{3}{2}} E - V}{V ^{2}} - \frac{4 E ( E - V ) ^{\frac{3}{2}}}{V ^{2}} + 1

求解步骤

\frac{( E - E - V ) ^{4}}{V ^{2}}

(E - E - V)^{4} = 8 E^{2} - 8 E V - 4 E^{\frac{3}{2}} E - V - 4 E (E - V)^{\frac{3}{2}} + V^{2}

= \frac{8 E ^{2} - 8 E V - 4 E ^{\frac{3}{2}} E - V - 4 E ( E - V ) ^{\frac{3}{2}} + V ^{2}}{V ^{2}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{8 E ^{2} - 8 E V - 4 E ^{\frac{3}{2}} E - V - 4 E ( E - V ) ^{\frac{3}{2}} + V ^{2}}{V ^{2}} = \frac{8 E ^{2}}{V ^{2}} - \frac{8 E V}{V ^{2}} - \frac{4 E ^{\frac{3}{2}} E - V}{V ^{2}} - \frac{4 E ( E - V ) ^{\frac{3}{2}}}{V ^{2}} + \frac{V ^{2}}{V ^{2}}

= \frac{8 E ^{2}}{V ^{2}} - \frac{8 E V}{V ^{2}} - \frac{4 E ^{\frac{3}{2}} E - V}{V ^{2}} - \frac{4 E ( E - V ) ^{\frac{3}{2}}}{V ^{2}} + \frac{V ^{2}}{V ^{2}}

使用法则

\frac{a}{a} = 1

\frac{V ^{2}}{V ^{2}} = 1

= \frac{8 E ^{2}}{V ^{2}} - \frac{8 E V}{V ^{2}} - \frac{4 E ^{\frac{3}{2}} E - V}{V ^{2}} - \frac{4 E ( E - V ) ^{\frac{3}{2}}}{V ^{2}} + 1

消掉

\frac{8 E V}{V ^{2}} : \frac{8 E}{V}

= \frac{8 E ^{2}}{V ^{2}} - \frac{8 E}{V} - \frac{4 E ^{\frac{3}{2}} E - V}{V ^{2}} - \frac{4 E ( E - V ) ^{\frac{3}{2}}}{V ^{2}} + 1

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