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人気のある代数 >

(ax+b)(cx-d)=4x^2-25

解

(a x + b) (c x - d) = 4 x^{2} - 25

解

x = \frac{a d - b c + a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}, x = \frac{a d - b c - a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}; a c - 4 \neq = 0

解答ステップ

(a x + b) (c x - d) = 4 x^{2} - 25

拡張

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

a c x^{2} - a d x + b c x - b d = 4 x^{2} - 25

25

を左側に移動します

a c x^{2} - a d x + b c x - b d + 25 = 4 x^{2}

4 x^{2}

を左側に移動します

a c x^{2} - a d x + b c x - b d + 25 - 4 x^{2} = 0

標準的な形式で書く

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

(a c - 4) x^{2} + (- a d + b c) x - b d + 25 = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - a d + b c ) \pm ( - a d + b c ) ^{2} - 4 ( a c - 4 ) ( - b d + 25 )}{2 ( a c - 4 )}

簡素化

(- a d + b c)^{2} - 4 (a c - 4) (- b d + 25) : a^{2} d^{2} - 100 a c + 2 ab c d + b^{2} c^{2} - 16 b d + 400

x_{1, 2} = \frac{- ( - a d + b c ) \pm a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}; a c - 4 \neq = 0

解を分離する

x_{1} = \frac{- ( - a d + b c ) + a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}, x_{2} = \frac{- ( - a d + b c ) - a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}

x = \frac{- ( - a d + b c ) + a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )} : \frac{a d - b c + a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}

x = \frac{- ( - a d + b c ) - a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )} : \frac{a d - b c - a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}

二次equationの解:

x = \frac{a d - b c + a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}, x = \frac{a d - b c - a ^{2} d ^{2} - 100 a c + 2 ab c d + b ^{2} c ^{2} - 16 b d + 400}{2 ( a c - 4 )}; a c - 4 \neq = 0

グラフ

人気の例

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