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人気のある代数 >

x^{12}=2

解

x^{12} = 2

解

x = 62, x = - 62, x = 62 i, x = - 62 i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} + 0.52973 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} - 0.52973 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} + 0.91752 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} - 0.91752 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} + 0.91752 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} - 0.91752 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} + 0.52973 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} - 0.52973 \dots i

解答ステップ

x^{12} = 2

equationを

u = x^{2}

と以下で書き換える:

u^{6} = x^{12}

u^{6} = 2

解く

u^{6} = 2 : u = 32, u = - 32, u = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, u = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, u = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, u = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i

u = 32, u = - 32, u = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, u = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, u = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, u = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 32 : x = 62, x = - 62

解く

x^{2} = - 32 : x = 62 i, x = - 62 i

解く

x^{2} = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i : x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} + 0.52973 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} - 0.52973 \dots i

解く

x^{2} = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i : x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} + 0.91752 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} - 0.91752 \dots i

解く

x^{2} = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i : x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} + 0.91752 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} - 0.91752 \dots i

解く

x^{2} = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i : x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} + 0.52973 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} - 0.52973 \dots i

解答は

x = 62, x = - 62, x = 62 i, x = - 62 i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} + 0.52973 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} - 0.52973 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} + 0.91752 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} - 0.91752 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} + 0.91752 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.83504 \dots} - 0.91752 \dots i, x = - \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} + 0.52973 \dots i, x = \frac{3}{2 ^{\frac{5}{6}} \cdot 1.05946 \dots} - 0.52973 \dots i

グラフ

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