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人気のある代数 >

solvefor x,f= 5/3 m^4x^2-7m^3x-3m

解

解く

x, f = \frac{5}{3} m^{4} x^{2} - 7 m^{3} x - 3 m

解

x = \frac{21 m + 3 147 m ^{2} + 20 ( f + 3 m )}{10 m ^{2}}, x = \frac{21 m - 3 147 m ^{2} + 20 ( f + 3 m )}{10 m ^{2}}; m \neq = 0

解答ステップ

f = \frac{5}{3} m^{4} x^{2} - 7 m^{3} x - 3 m

以下で両辺を乗じる:

3

3 f = 5 m^{4} x^{2} - 21 m^{3} x - 9 m

辺を交換する

5 m^{4} x^{2} - 21 m^{3} x - 9 m = 3 f

3 f

を左側に移動します

5 m^{4} x^{2} - 21 m^{3} x - 9 m - 3 f = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 21 m ^{3} ) \pm ( - 21 m ^{3} ) ^{2} - 4 \cdot 5 m ^{4} ( - 9 m - 3 f )}{2 \cdot 5 m ^{4}}

簡素化

(- 21 m^{3})^{2} - 4 \cdot 5 m^{4} (- 9 m - 3 f) : 3 m^{2} 147 m^{2} + 20 (f + 3 m)

x_{1, 2} = \frac{- ( - 21 m ^{3} ) \pm 3 m ^{2} 147 m ^{2} + 20 ( f + 3 m )}{2 \cdot 5 m ^{4}}; m \neq = 0

解を分離する

x_{1} = \frac{- ( - 21 m ^{3} ) + 3 m ^{2} 147 m ^{2} + 20 ( f + 3 m )}{2 \cdot 5 m ^{4}}, x_{2} = \frac{- ( - 21 m ^{3} ) - 3 m ^{2} 147 m ^{2} + 20 ( f + 3 m )}{2 \cdot 5 m ^{4}}

x = \frac{- ( - 21 m ^{3} ) + 3 m ^{2} 147 m ^{2} + 20 ( f + 3 m )}{2 \cdot 5 m ^{4}} : \frac{21 m + 3 147 m ^{2} + 20 ( f + 3 m )}{10 m ^{2}}

x = \frac{- ( - 21 m ^{3} ) - 3 m ^{2} 147 m ^{2} + 20 ( f + 3 m )}{2 \cdot 5 m ^{4}} : \frac{21 m - 3 147 m ^{2} + 20 ( f + 3 m )}{10 m ^{2}}

二次equationの解:

x = \frac{21 m + 3 147 m ^{2} + 20 ( f + 3 m )}{10 m ^{2}}, x = \frac{21 m - 3 147 m ^{2} + 20 ( f + 3 m )}{10 m ^{2}}; m \neq = 0

グラフ

人気の例

u^{2} - 7 u - 18 = 0

x^{2} + 3 x = x + 7

x^{2} = 1 3^{2} - 1 2^{2}

5 x^{2} - 2 x - 2 = 0

3 x^{2} - 17 = 0