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受欢迎的代数 >

solvefor m,x^2+m(x)^2x(m(x)-2)=2m(x)^5

解答

求解

m, x^{2} + m (x)^{2} x (m (x) - 2) = 2 m (x)^{5}

解答

m = \frac{1 + x ^{2} + x x ^{2} + 2}{x}, m = \frac{1 + x ^{2} - x x ^{2} + 2}{x}; x \neq = 0

求解步骤

x^{2} + m x^{2} x (m (x) - 2) = 2 m x^{5}

展开

x^{2} + m x^{2} x (m (x) - 2) : x^{2} + m^{2} x^{4} - 2 m x^{3}

x^{2} + m^{2} x^{4} - 2 m x^{3} = 2 m x^{5}

将

2 m x^{5}

para o lado esquerdo

x^{2} + m^{2} x^{4} - 2 m x^{3} - 2 m x^{5} = 0

改写成标准形式

a x^{2} + b x + c = 0

x^{4} m^{2} - (2 x^{3} + 2 x^{5}) m + x^{2} = 0

使用求根公式求解

m_{1, 2} = \frac{- ( - 2 x ^{3} - 2 x ^{5} ) \pm ( - 2 x ^{3} - 2 x ^{5} ) ^{2} - 4 x ^{4} x ^{2}}{2 x ^{4}}

化简

(- 2 x^{3} - 2 x^{5})^{2} - 4 x^{4} x^{2} : 2 x^{4} x^{2} + 2

m_{1, 2} = \frac{- ( - 2 x ^{3} - 2 x ^{5} ) \pm 2 x ^{4} x ^{2} + 2}{2 x ^{4}}; x \neq = 0

将解分隔开

m_{1} = \frac{- ( - 2 x ^{3} - 2 x ^{5} ) + 2 x ^{4} x ^{2} + 2}{2 x ^{4}}, m_{2} = \frac{- ( - 2 x ^{3} - 2 x ^{5} ) - 2 x ^{4} x ^{2} + 2}{2 x ^{4}}

m = \frac{- ( - 2 x ^{3} - 2 x ^{5} ) + 2 x ^{4} x ^{2} + 2}{2 x ^{4}} : \frac{1 + x ^{2} + x x ^{2} + 2}{x}

m = \frac{- ( - 2 x ^{3} - 2 x ^{5} ) - 2 x ^{4} x ^{2} + 2}{2 x ^{4}} : \frac{1 + x ^{2} - x x ^{2} + 2}{x}

二次方程组的解是:

m = \frac{1 + x ^{2} + x x ^{2} + 2}{x}, m = \frac{1 + x ^{2} - x x ^{2} + 2}{x}; x \neq = 0

作图

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