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受欢迎的代数 >

3sqrt(x)+3x^{-1/2}=10

解答

3 x + 3 x^{- \frac{1}{2}} = 10

解答

x = 9, x = \frac{1}{9}

+1

十进制

x = 9, x = 0.11111 \dots

求解步骤

3 x + 3 x^{- \frac{1}{2}} = 10

展开

3 x + 3 x^{- \frac{1}{2}} : 3 x + \frac{3}{x ^{\frac{1}{2}}}

3 x + \frac{3}{x ^{\frac{1}{2}}} = 10

去除平方根

81 x^{2} - 1800 x + \frac{81}{x ^{2}} + \frac{1800}{x} + 9838 = \frac{3600}{x}

解

81 x^{2} - 1800 x + \frac{81}{x ^{2}} + \frac{1800}{x} + 9838 = \frac{3600}{x} : x = 9, x = \frac{1}{9}, x = \frac{59 + 10 \cdot 3 4 ^{\frac{1}{2}}}{9}, x = \frac{59 - 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

x = 9, x = \frac{1}{9}, x = \frac{59 + 10 \cdot 3 4 ^{\frac{1}{2}}}{9}, x = \frac{59 - 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

验证解:

x = 9

真

, x = \frac{1}{9}

真

, x = \frac{59 + 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

假

, x = \frac{59 - 10 \cdot 3 4 ^{\frac{1}{2}}}{9}

假

解为

x = 9, x = \frac{1}{9}

作图

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