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受欢迎的代数 >

130r^3-a^2r^3+a^2=0

解答

130 r^{3} - a^{2} r^{3} + a^{2} = 0

解答

r = - 3 \frac{a ^{2}}{130 - a ^{2}}, r = - \frac{3 a ^{2} ( - 1 + 3 i )}{2 3 130 - a ^{2}}, r = - \frac{3 a ^{2} ( - 1 - 3 i )}{2 3 130 - a ^{2}}; a \neq = 130, a \neq = - 130

求解步骤

130 r^{3} - a^{2} r^{3} + a^{2} = 0

将

a^{2}

到右边

130 r^{3} - a^{2} r^{3} = - a^{2}

分解

130 r^{3} - a^{2} r^{3} : r^{3} (130 - a^{2})

r^{3} (130 - a^{2}) = - a^{2}

两边除以

130 - a^{2}; a \neq = 130, a \neq = - 130

r^{3} = - \frac{a ^{2}}{130 - a ^{2}}; a \neq = 130, a \neq = - 130

对于

x^{3} = f (a)

解为

x = 3 f (a), 3 f (a) \frac{- 1 - 3 i}{2}, 3 f (a) \frac{- 1 + 3 i}{2}

r = 3 - \frac{a ^{2}}{130 - a ^{2}}, r = 3 - \frac{a ^{2}}{130 - a ^{2}} \frac{- 1 + 3 i}{2}, r = 3 - \frac{a ^{2}}{130 - a ^{2}} \frac{- 1 - 3 i}{2}; a \neq = 130, a \neq = - 130

化简

3 - \frac{a ^{2}}{130 - a ^{2}} : - 3 \frac{a ^{2}}{130 - a ^{2}}

化简

3 - \frac{a ^{2}}{130 - a ^{2}} \frac{- 1 + 3 i}{2} : - \frac{3 a ^{2} ( - 1 + 3 i )}{2 3 130 - a ^{2}}

化简

3 - \frac{a ^{2}}{130 - a ^{2}} \frac{- 1 - 3 i}{2} : - \frac{3 a ^{2} ( - 1 - 3 i )}{2 3 130 - a ^{2}}

r = - 3 \frac{a ^{2}}{130 - a ^{2}}, r = - \frac{3 a ^{2} ( - 1 + 3 i )}{2 3 130 - a ^{2}}, r = - \frac{3 a ^{2} ( - 1 - 3 i )}{2 3 130 - a ^{2}}; a \neq = 130, a \neq = - 130

作图

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