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人気のある代数 >

x^{4/3}-5x^{2/3}+6=0

解

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} + 6 = 0

解

x = 3 \cdot 3^{\frac{1}{2}}, x = - 3 \cdot 3^{\frac{1}{2}}, x = 2 \cdot 2^{\frac{1}{2}}, x = - 2 \cdot 2^{\frac{1}{2}}

+1

十進法表記

x = 5.19615 \dots, x = - 5.19615 \dots, x = 2.82842 \dots, x = - 2.82842 \dots

解答ステップ

x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} + 6 = 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}

(x^{\frac{1}{3}})^{4} - 5 (x^{\frac{1}{3}})^{2} + 6 = 0

equationを以下で書き換える:

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

u^{4} - 5 u^{2} + 6 = 0

解く

u^{4} - 5 u^{2} + 6 = 0 : u = 3, u = - 3, u = 2, u = - 2

u = 3, u = - 3, u = 2, u = - 2

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}} = 3 : x = 3 \cdot 3^{\frac{1}{2}}

解く

x^{\frac{1}{3}} = - 3 : x = - 3 \cdot 3^{\frac{1}{2}}

解く

x^{\frac{1}{3}} = 2 : x = 2 \cdot 2^{\frac{1}{2}}

解く

x^{\frac{1}{3}} = - 2 : x = - 2 \cdot 2^{\frac{1}{2}}

x = 3 \cdot 3^{\frac{1}{2}}, x = - 3 \cdot 3^{\frac{1}{2}}, x = 2 \cdot 2^{\frac{1}{2}}, x = - 2 \cdot 2^{\frac{1}{2}}

解を検算する:

x = 3 \cdot 3^{\frac{1}{2}}

真

, x = - 3 \cdot 3^{\frac{1}{2}}

真

, x = 2 \cdot 2^{\frac{1}{2}}

真

, x = - 2 \cdot 2^{\frac{1}{2}}

真

解答は

x = 3 \cdot 3^{\frac{1}{2}}, x = - 3 \cdot 3^{\frac{1}{2}}, x = 2 \cdot 2^{\frac{1}{2}}, x = - 2 \cdot 2^{\frac{1}{2}}

グラフ

人気の例

x+sqrt(20+2x)=2

x + 20 + 2 x = 2

2 + x = x

sqrt(3x+16)=x+2

3 x + 16 = x + 2

7 x - 7 = x - 1

sqrt(2x+3)+sqrt(x-5)=0

2 x + 3 + x - 5 = 0