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受欢迎的代数 >

x^9+x^6=36

解答

x^{9} + x^{6} = 36

解答

x = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i, x = 3263 cos (\frac{- arctan ( 2 ) + π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + π}{3}), x = 3263 cos (\frac{- arctan ( 2 ) + 3 π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + 3 π}{3}), x = 3263 cos (\frac{- arctan ( 2 ) + 5 π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + 5 π}{3}), x = 3263 cos (\frac{arctan ( 2 ) - π}{3}) + 3263 i sin (\frac{arctan ( 2 ) - π}{3}), x = 3263 cos (\frac{arctan ( 2 ) + π}{3}) + 3263 i sin (\frac{arctan ( 2 ) + π}{3}), x = 3263 cos (\frac{arctan ( 2 ) + 3 π}{3}) + 3263 i sin (\frac{arctan ( 2 ) + 3 π}{3})

求解步骤

x^{9} + x^{6} = 36

将

36

para o lado esquerdo

x^{9} + x^{6} - 36 = 0

用

u = x^{3}, u^{2} = x^{6}

和

u^{3} = x^{9}

改写方程式

u^{3} + u^{2} - 36 = 0

解

u^{3} + u^{2} - 36 = 0 : u = 3, u = - 2 + 22 i, u = - 2 - 22 i

u = 3, u = - 2 + 22 i, u = - 2 - 22 i

代回

u = x^{3}

，求解

x

解

x^{3} = 3 : x = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i

解

x^{3} = - 2 + 22 i : x = 3263 cos (\frac{- arctan ( 2 ) + π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + π}{3}), x = 3263 cos (\frac{- arctan ( 2 ) + 3 π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + 3 π}{3}), x = 3263 cos (\frac{- arctan ( 2 ) + 5 π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + 5 π}{3})

解

x^{3} = - 2 - 22 i : x = 3263 cos (\frac{arctan ( 2 ) - π}{3}) + 3263 i sin (\frac{arctan ( 2 ) - π}{3}), x = 3263 cos (\frac{arctan ( 2 ) + π}{3}) + 3263 i sin (\frac{arctan ( 2 ) + π}{3}), x = 3263 cos (\frac{arctan ( 2 ) + 3 π}{3}) + 3263 i sin (\frac{arctan ( 2 ) + 3 π}{3})

解为

x = 33, x = - 33 \frac{1}{2} + 33 \frac{3}{2} i, x = - 33 \frac{1}{2} - 33 \frac{3}{2} i, x = 3263 cos (\frac{- arctan ( 2 ) + π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + π}{3}), x = 3263 cos (\frac{- arctan ( 2 ) + 3 π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + 3 π}{3}), x = 3263 cos (\frac{- arctan ( 2 ) + 5 π}{3}) + 3263 i sin (\frac{- arctan ( 2 ) + 5 π}{3}), x = 3263 cos (\frac{arctan ( 2 ) - π}{3}) + 3263 i sin (\frac{arctan ( 2 ) - π}{3}), x = 3263 cos (\frac{arctan ( 2 ) + π}{3}) + 3263 i sin (\frac{arctan ( 2 ) + π}{3}), x = 3263 cos (\frac{arctan ( 2 ) + 3 π}{3}) + 3263 i sin (\frac{arctan ( 2 ) + 3 π}{3})

作图

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