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人気のある代数 >

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

解

解く

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

解

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

解答ステップ

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

拡張

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}

2 m x^{5}

を左側に移動します

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

標準的な形式で書く

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

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

解くとthe二次式

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}}

簡素化

(- 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

解を分離する

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equationの解:

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

グラフ

人気の例

x^{2} - 5 x + 17 = 11

3 x^{2} - 32 x + 69 = 0

2 n^{2} - 9 n + 5 = 2 n

completesquare 2x^2+12x+8

co m pl e t es q u a re 2 x^{2} + 12 x + 8

6 w^{2} - 26 w + 5 = w^{2}