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人気のある代数 >

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

解

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

解

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

解答ステップ

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

拡張

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

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

標準的な形式で書く

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

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

解くとthe二次式

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

簡素化

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

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

解を分離する

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

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

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

二次equationの解:

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

グラフ

人気の例

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