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

解

解く

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

x = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}, x = - a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

解答ステップ

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

y^{\frac{2}{3}}

を右側に移動します

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

equationの両辺を以下の累乗にする:

3 : x^{2} = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

x^{2} = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

解く

x^{2} = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2} : x = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}, x = - a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}

x = a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}, x = - a^{2} - 3 a^{\frac{4}{3}} y^{\frac{2}{3}} + 3 a^{\frac{2}{3}} y^{\frac{4}{3}} - y^{2}