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인기 있는 대수학 >

x^{12}=5000

해법

x^{12} = 5000

해법

x = 3252, x = - 3252, x = - 3252, x = - - 3252, x = - 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = - 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

솔루션 단계

x^{12} = 5000

다음으로 방정식 다시 쓰기

u = x^{2}

그리고

u^{6} = x^{12}

u^{6} = 5000

u^{6} = 5000

해결 :

u = 3 5^{2} 2, u = - 3 5^{2} 2, u = - \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = - \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i

u = 3 5^{2} 2, u = - 3 5^{2} 2, u = - \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i, u = \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i, u = - \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i

다시 대체

u = x^{2},

을 해결하다

x

x^{2} = 3 5^{2} 2

해결 :

x = 3252, x = - 3252

x^{2} = - 3 5^{2} 2

해결 :

x = - 3252, x = - - 3252

x^{2} = - \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i

해결 :

x = - 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

x^{2} = \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i

해결 :

x = 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i

x^{2} = \frac{5 3 5 3}{7.16235 \dots} - 3.58117 \dots i

해결 :

x = - 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i

x^{2} = - \frac{5 3 5 3}{7.16235 \dots} + 3.58117 \dots i

해결 :

x = 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = - 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

해결책은

x = 3252, x = - 3252, x = - 3252, x = - - 3252, x = - 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = - 1.76107 \dots + \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.76107 \dots - \frac{17.09975 \dots - 2.06759 \dots}{2} i, x = 1.01675 \dots + \frac{2.06759 \dots + 17.09975 \dots}{2} i, x = - 1.01675 \dots - \frac{2.06759 \dots + 17.09975 \dots}{2} i

그래프

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