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人気のある代数 >

ab(x^2-c^2)=(a^2-b^2)cx

解

ab (x^{2} - c^{2}) = (a^{2} - b^{2}) c x

解

x = \frac{a c}{b}, x = - \frac{b c}{a}; ab \neq = 0

解答ステップ

ab (x^{2} - c^{2}) = (a^{2} - b^{2}) c x

拡張

ab (x^{2} - c^{2}) : ab x^{2} - ab c^{2}

拡張

(a^{2} - b^{2}) c x : a^{2} c x - b^{2} c x

ab x^{2} - ab c^{2} = a^{2} c x - b^{2} c x

b^{2} c x

を左側に移動します

ab x^{2} - ab c^{2} + b^{2} c x = a^{2} c x

a^{2} c x

を左側に移動します

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

標準的な形式で書く

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

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

解くとthe二次式

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

簡素化

(b^{2} c - a^{2} c)^{2} - 4 ab (- ab c^{2}) : c (a^{2} + b^{2})

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

解を分離する

x_{1} = \frac{- ( b ^{2} c - a ^{2} c ) + c ( a ^{2} + b ^{2} )}{2 ab}, x_{2} = \frac{- ( b ^{2} c - a ^{2} c ) - c ( a ^{2} + b ^{2} )}{2 ab}

x = \frac{- ( b ^{2} c - a ^{2} c ) + c ( a ^{2} + b ^{2} )}{2 ab} : \frac{a c}{b}

x = \frac{- ( b ^{2} c - a ^{2} c ) - c ( a ^{2} + b ^{2} )}{2 ab} : - \frac{b c}{a}

二次equationの解:

x = \frac{a c}{b}, x = - \frac{b c}{a}; ab \neq = 0

グラフ

人気の例

x^{2} + x - 22 = 8

4 d^{2} + 9 d - 7 = 2

x^2-160x+10000=0

x^{2} - 160 x + 10000 = 0

x^{2} - 6 x = 2 x

x^{2} - 9 x + 3 = 3