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人気のある代数 >

81=1.5^2× x^9

解

81 = 1. 5^{2} \cdot x^{9}

解

x = 3336, x = - 3336 \frac{1}{2} + 3336 \frac{3}{2} i, x = - 3336 \frac{1}{2} - 3336 \frac{3}{2} i, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}}

解答ステップ

81 = 1. 5^{2} x^{9}

辺を交換する

1. 5^{2} x^{9} = 81

以下で両辺を割る

2.25

x^{9} = 36

equationを

u = x^{3}

と以下で書き換える:

u^{3} = x^{9}

u^{3} = 36

解く

u^{3} = 36 : u = 336, u = 336 \frac{- 1 + 3 i}{2}, u = 336 \frac{- 1 - 3 i}{2}

u = 336, u = 336 \frac{- 1 + 3 i}{2}, u = 336 \frac{- 1 - 3 i}{2}

再び

u = x^{3}

に置き換えて以下を解く:

x

解く

x^{3} = 336 : x = 3336, x = - 3336 \frac{1}{2} + 3336 \frac{3}{2} i, x = - 3336 \frac{1}{2} - 3336 \frac{3}{2} i

解く

x^{3} = 336 \frac{- 1 + 3 i}{2} : x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}}

解く

x^{3} = 336 \frac{- 1 - 3 i}{2} : x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}}

解答は

x = 3336, x = - 3336 \frac{1}{2} + 3336 \frac{3}{2} i, x = - 3336 \frac{1}{2} - 3336 \frac{3}{2} i, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{8 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{14 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}} - i sin (\frac{2 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{4 π}{9}) 6 3 6^{\frac{2}{3}}, x = cos (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}} + i sin (\frac{10 π}{9}) 6 3 6^{\frac{2}{3}}

グラフ

人気の例

因数 x^3-8x^2+22x-21=0

f a c t or x^{3} - 8 x^{2} + 22 x - 21 = 0

solvefor y,x^4+y^4=0

so l v e f or y, x^{4} + y^{4} = 0

因数 m^3+3m^2-4=0

f a c t or m^{3} + 3 m^{2} - 4 = 0

3x^3-17x^2+18x+8=0

3 x^{3} - 17 x^{2} + 18 x + 8 = 0

solvefor f,fx=4x^3-6x^2

so l v e f or f, f x = 4 x^{3} - 6 x^{2}