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人気のある代数 >

9x^{4/3}-10x^{2/3}+1=0

解

9 x^{\frac{4}{3}} - 10 x^{\frac{2}{3}} + 1 = 0

解

x = 1, x = - 1, x = \frac{1}{27}, x = - \frac{1}{27}

+1

十進法表記

x = 1, x = - 1, x = 0.03703 \dots, x = - 0.03703 \dots

解答ステップ

9 x^{\frac{4}{3}} - 10 x^{\frac{2}{3}} + 1 = 0

以下のべき指数プロパティを使用する

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{4}{3}} = (x^{\frac{1}{3}})^{4}, x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

9 (x^{\frac{1}{3}})^{4} - 10 (x^{\frac{1}{3}})^{2} + 1 = 0

equationを以下で書き換える:

x^{\frac{1}{3}} = u

9 u^{4} - 10 u^{2} + 1 = 0

解く

9 u^{4} - 10 u^{2} + 1 = 0 : u = 1, u = - 1, u = \frac{1}{3}, u = - \frac{1}{3}

u = 1, u = - 1, u = \frac{1}{3}, u = - \frac{1}{3}

再び

u = x^{\frac{1}{3}}

に置き換えて以下を解く:

x

解く

x^{\frac{1}{3}} = 1 : x = 1

解く

x^{\frac{1}{3}} = - 1 : x = - 1

解く

x^{\frac{1}{3}} = \frac{1}{3} : x = \frac{1}{27}

解く

x^{\frac{1}{3}} = - \frac{1}{3} : x = - \frac{1}{27}

x = 1, x = - 1, x = \frac{1}{27}, x = - \frac{1}{27}

解を検算する:

x = 1

真

, x = - 1

真

, x = \frac{1}{27}

真

, x = - \frac{1}{27}

真

解答は

x = 1, x = - 1, x = \frac{1}{27}, x = - \frac{1}{27}

グラフ

人気の例

sqrt(-72+17x)=x

- 72 + 17 x = x

2x^{2/3}+x^{1/3}-1=0

2 x^{\frac{2}{3}} + x^{\frac{1}{3}} - 1 = 0

x = 9 x - 10

(\sqrt[4]{7w-5})/2 =\sqrt[4]{w-2}

\frac{4 7 w - 5}{2} = 4 w - 2

cube root of 3x-4}=\sqrt[3]{x-3

3 3 x - 4 = 3 x - 3