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人気のある代数 >

solvefor m,2(mx-1)^2=m(2x-1)^2

解

解く

m, 2 (m x - 1)^{2} = m (2 x - 1)^{2}

解

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

解答ステップ

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

拡張

2 (m x - 1)^{2} : 2 m^{2} x^{2} - 4 m x + 2

拡張

m (2 x - 1)^{2} : 4 m x^{2} - 4 m x + m

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

両辺から

- 4 m x + m

を引く

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

簡素化

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

4 m x^{2}

を左側に移動します

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

標準的な形式で書く

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

2 x^{2} m^{2} - (1 + 4 x^{2}) m + 2 = 0

解くとthe二次式

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

簡素化

(- 1 - 4 x^{2})^{2} - 4 \cdot 2 x^{2} \cdot 2 : (2 x + 1) (2 x - 1)

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

解を分離する

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

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

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

二次equationの解:

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

グラフ

人気の例

7 x^{2} + 11 x - 6 = 0

z^{2} + 3 = 0

x^{2} - 16 x + 20 = 0

x^{2} + 7 x = 10

6 n^{2} - 19 n + 15 = 0