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

解答

求解

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}

求解步骤

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

将

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

到右边

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

对方程式两边

3

次方:

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

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}

x + 2 = 2 x + 1

x - 1 - 2 x + 1 = 0

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

3 x - 27 = 0

x^{\frac{3}{2}} + (x^{2})^{- 2} + x^{3} = 4