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인기 있는 대수학 >

a=(x^3+1)(x^6-x^3+1)

해법

a = (x^{3} + 1) (x^{6} - x^{3} + 1)

해법

x = 3 3 a - 1, x = - \frac{3 3 a - 1}{2} + \frac{3 3 a - 1 3}{2} i, x = - \frac{3 3 a - 1}{2} - \frac{3 3 a - 1 3}{2} i, x = cos (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}} - i sin (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{5 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{5 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{11 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{11 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{7 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{7 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{13 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{13 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}

솔루션 단계

a = (x^{3} + 1) (x^{6} - x^{3} + 1)

(x^{3} + 1) (x^{6} - x^{3} + 1)

확장 :

x^{9} + 1

a = x^{9} + 1

측면 전환

x^{9} + 1 = a

a

를 왼쪽으로 이동

x^{9} + 1 - a = 0

다음으로 방정식 다시 쓰기

u = x^{3}

그리고

u^{3} = x^{9}

u^{3} + 1 - a = 0

u^{3} + 1 - a = 0

해결 :

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

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

다시 대체

u = x^{3},

을 해결하다

x

x^{3} = 3 a - 1

해결 :

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

x^{3} = 3 a - 1 \frac{- 1 + 3 i}{2}

해결 :

x = cos (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}} - i sin (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{5 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{5 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{11 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{11 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}

x^{3} = 3 a - 1 \frac{- 1 - 3 i}{2}

해결 :

x = cos (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{7 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{7 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{13 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{13 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}

해결책은

x = 3 3 a - 1, x = - \frac{3 3 a - 1}{2} + \frac{3 3 a - 1 3}{2} i, x = - \frac{3 3 a - 1}{2} - \frac{3 3 a - 1 3}{2} i, x = cos (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}} - i sin (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{5 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{5 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{11 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{11 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{7 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{7 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}, x = cos (\frac{13 π}{9}) 6 (- 1 + a)^{\frac{2}{3}} + i sin (\frac{13 π}{9}) 6 (- 1 + a)^{\frac{2}{3}}

그래프

인기 있는 예

16y^4-55y^2-36=0

16 y^{4} - 55 y^{2} - 36 = 0

4 x^{3} - 2 x^{2} = 0

x^{4} = 1

x^{3} + x + 1 = 0

x^{3} = - 1