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受欢迎的代数 >

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

解答

求解

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

解答

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}}}

求解步骤

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

将

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

到右边

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

对方程式两边

3

次方:

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

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}

验证解:

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}}}

解为

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}}}

作图

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