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人気のある代数 >

(a-x)^3+(x-b)^3=(a-b)^3

解

(a - x)^{3} + (x - b)^{3} = (a - b)^{3}

解

x = \frac{a ^{2} - b ^{2} + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}, x = \frac{a ^{2} - b ^{2} - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}; 3 a - 3 b \neq = 0

解答ステップ

(a - x)^{3} + (x - b)^{3} = (a - b)^{3}

拡張

(a - x)^{3} + (x - b)^{3} : a^{3} - 3 a^{2} x + 3 a x^{2} - 3 b x^{2} + 3 b^{2} x - b^{3}

拡張

(a - b)^{3} : a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a^{3} - 3 a^{2} x + 3 a x^{2} - 3 b x^{2} + 3 b^{2} x - b^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

b^{3}

を左側に移動します

a^{3} - 3 a^{2} x + 3 a x^{2} - 3 b x^{2} + 3 b^{2} x = a^{3} - 3 a^{2} b + 3 a b^{2}

3 a b^{2}

を左側に移動します

a^{3} - 3 a^{2} x + 3 a x^{2} - 3 b x^{2} + 3 b^{2} x - 3 a b^{2} = a^{3} - 3 a^{2} b

3 a^{2} b

を左側に移動します

a^{3} - 3 a^{2} x + 3 a x^{2} - 3 b x^{2} + 3 b^{2} x - 3 a b^{2} + 3 a^{2} b = a^{3}

a^{3}

を左側に移動します

3 a x^{2} - 3 b x^{2} - 3 a^{2} x + 3 b^{2} x - 3 a b^{2} + 3 a^{2} b = 0

標準的な形式で書く

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

(3 a - 3 b) x^{2} + (- 3 a^{2} + 3 b^{2}) x - 3 a b^{2} + 3 a^{2} b = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 3 a ^{2} + 3 b ^{2} ) \pm ( - 3 a ^{2} + 3 b ^{2} ) ^{2} - 4 ( 3 a - 3 b ) ( - 3 a b ^{2} + 3 a ^{2} b )}{2 ( 3 a - 3 b )}

簡素化

(- 3 a^{2} + 3 b^{2})^{2} - 4 (3 a - 3 b) (- 3 a b^{2} + 3 a^{2} b) : 3 a^{4} - 4 a^{3} b + 6 a^{2} b^{2} - 4 a b^{3} + b^{4}

x_{1, 2} = \frac{- ( - 3 a ^{2} + 3 b ^{2} ) \pm 3 a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( 3 a - 3 b )}; 3 a - 3 b \neq = 0

解を分離する

x_{1} = \frac{- ( - 3 a ^{2} + 3 b ^{2} ) + 3 a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( 3 a - 3 b )}, x_{2} = \frac{- ( - 3 a ^{2} + 3 b ^{2} ) - 3 a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( 3 a - 3 b )}

x = \frac{- ( - 3 a ^{2} + 3 b ^{2} ) + 3 a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( 3 a - 3 b )} : \frac{a ^{2} - b ^{2} + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}

x = \frac{- ( - 3 a ^{2} + 3 b ^{2} ) - 3 a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( 3 a - 3 b )} : \frac{a ^{2} - b ^{2} - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}

二次equationの解:

x = \frac{a ^{2} - b ^{2} + a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}, x = \frac{a ^{2} - b ^{2} - a ^{4} - 4 a ^{3} b + 6 a ^{2} b ^{2} - 4 a b ^{3} + b ^{4}}{2 ( a - b )}; 3 a - 3 b \neq = 0

グラフ

人気の例

x^{2} + 1 = 2 x + 1

3 x^{2} + 6 x + 10 = 0

completesquare s^2+2s+10

co m pl e t es q u a re s^{2} + 2 s + 10

(x^2)/(10)-x/5+2=0

\frac{x ^{2}}{10} - \frac{x}{5} + 2 = 0

solvefor x,x^2=-y^2

so l v e f or x, x^{2} = - y^{2}