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人気のある代数 >

solvefor y,x^{2/3}+y^{2/3}=5

解

解く

y, x^{\frac{2}{3}} + y^{\frac{2}{3}} = 5

解

y = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2} {- 5 \cdot 5^{\frac{1}{2}} < x < 5 \cdot 5^{\frac{1}{2}}}, y = - 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2} {- 5 \cdot 5^{\frac{1}{2}} < x < 5 \cdot 5^{\frac{1}{2}}}

解答ステップ

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 5

x^{\frac{2}{3}}

を右側に移動します

y^{\frac{2}{3}} = 5 - x^{\frac{2}{3}}

equationの両辺を以下の累乗にする:

3 : y^{2} = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2}

y^{2} = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2}

解く

y^{2} = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2} : y = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2}, y = - 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2}

y = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2}, y = - 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2}

解を検算する:

y = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2} {- 5 \cdot 5^{\frac{1}{2}} < x < 5 \cdot 5^{\frac{1}{2}}}, y = - 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2} {- 5 \cdot 5^{\frac{1}{2}} < x < 5 \cdot 5^{\frac{1}{2}}}

解答は

y = 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2} {- 5 \cdot 5^{\frac{1}{2}} < x < 5 \cdot 5^{\frac{1}{2}}}, y = - 125 - 75 x^{\frac{2}{3}} + 15 x^{\frac{4}{3}} - x^{2} {- 5 \cdot 5^{\frac{1}{2}} < x < 5 \cdot 5^{\frac{1}{2}}}

グラフ

人気の例

4 w + 4 = - 4

-2x^{3/4}+47=-7

- 2 x^{\frac{3}{4}} + 47 = - 7

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

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

sqrt(x-3)=1+sqrt(x-4)

x - 3 = 1 + x - 4

sqrt(n-1)+2=sqrt(3n+3)

n - 1 + 2 = 3 n + 3