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受欢迎的代数 >

x^2+(x/(x-1))^2=1

解答

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

解答

x \approx 0.46898 \dots, x \approx - 0.88320 \dots

求解步骤

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

化简

(\frac{x}{x - 1})^{2} : \frac{x ^{2}}{( x - 1 ) ^{2}}

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

在两边乘以

(x - 1)^{2}

x^{2} (x - 1)^{2} + x^{2} = (x - 1)^{2}

解

x^{2} (x - 1)^{2} + x^{2} = (x - 1)^{2} : x \approx 0.46898 \dots, x \approx - 0.88320 \dots

x \approx 0.46898 \dots, x \approx - 0.88320 \dots

验证解

找到无定义的点（奇点）:

x = 1

将不在定义域的点与解相综合:

x \approx 0.46898 \dots, x \approx - 0.88320 \dots

作图

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