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受欢迎的代数 >

solvefor y,x^2y^9=2

解答

求解

y, x^{2} y^{9} = 2

解答

y = 3 3 \frac{2}{y ^{2}}, y = - \frac{3 3 \frac{2}{y ^{2}}}{2} + \frac{3 3 \frac{2}{y ^{2}} 3}{2} i, y = - \frac{3 3 \frac{2}{y ^{2}}}{2} - \frac{3 3 \frac{2}{y ^{2}} 3}{2} i, y = cos (\frac{π}{9}) 18 \frac{4}{y ^{4}} - i sin (\frac{π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{5 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{5 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{11 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{11 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{7 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{7 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{13 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{13 π}{9}) 18 \frac{4}{y ^{4}}

求解步骤

y^{2} y^{9} = 2

两边除以

y^{2}; y \neq = 0

y^{9} = \frac{2}{y ^{2}}; y \neq = 0

用

u = y^{3}

和

u^{3} = y^{9}

改写方程式

u^{3} = \frac{2}{y ^{2}}

解

u^{3} = \frac{2}{y ^{2}} : u = 3 \frac{2}{y ^{2}}, u = 3 \frac{2}{y ^{2}} \frac{- 1 + 3 i}{2}, u = 3 \frac{2}{y ^{2}} \frac{- 1 - 3 i}{2}

u = 3 \frac{2}{y ^{2}}, u = 3 \frac{2}{y ^{2}} \frac{- 1 + 3 i}{2}, u = 3 \frac{2}{y ^{2}} \frac{- 1 - 3 i}{2}

代回

u = y^{3}

，求解

y

解

y^{3} = 3 \frac{2}{y ^{2}} : y = 3 3 \frac{2}{y ^{2}}, y = - \frac{3 3 \frac{2}{y ^{2}}}{2} + \frac{3 3 \frac{2}{y ^{2}} 3}{2} i, y = - \frac{3 3 \frac{2}{y ^{2}}}{2} - \frac{3 3 \frac{2}{y ^{2}} 3}{2} i

解

y^{3} = 3 \frac{2}{y ^{2}} \frac{- 1 + 3 i}{2} : y = cos (\frac{π}{9}) 18 \frac{4}{y ^{4}} - i sin (\frac{π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{5 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{5 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{11 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{11 π}{9}) 18 \frac{4}{y ^{4}}

解

y^{3} = 3 \frac{2}{y ^{2}} \frac{- 1 - 3 i}{2} : y = cos (\frac{π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{7 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{7 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{13 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{13 π}{9}) 18 \frac{4}{y ^{4}}

解为

y = 3 3 \frac{2}{y ^{2}}, y = - \frac{3 3 \frac{2}{y ^{2}}}{2} + \frac{3 3 \frac{2}{y ^{2}} 3}{2} i, y = - \frac{3 3 \frac{2}{y ^{2}}}{2} - \frac{3 3 \frac{2}{y ^{2}} 3}{2} i, y = cos (\frac{π}{9}) 18 \frac{4}{y ^{4}} - i sin (\frac{π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{5 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{5 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{11 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{11 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{7 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{7 π}{9}) 18 \frac{4}{y ^{4}}, y = cos (\frac{13 π}{9}) 18 \frac{4}{y ^{4}} + i sin (\frac{13 π}{9}) 18 \frac{4}{y ^{4}}

作图

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