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인기 있는 대수학 >

x^9+x^6=36

해법

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

해법

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})

솔루션 단계

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

36

를 왼쪽으로 이동

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

다음으로 방정식 다시 쓰기

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

그리고

u^{3} = x^{9}

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

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

해결 :

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

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

다시 대체

u = x^{3},

을 해결하다

x

x^{3} = 3

해결 :

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

x^{3} = - 2 + 22 i

해결 :

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^{3} = - 2 - 22 i

해결 :

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})

해결책은

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})

그래프

인기 있는 예

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