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人気のある代数 >

ax^2+bx+7=k(3x^2-2x+1)

解

a x^{2} + b x + 7 = k (3 x^{2} - 2 x + 1)

解

x = \frac{- b - 2 k + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}, x = \frac{- b - 2 k - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}; k \neq = \frac{a}{3}

解答ステップ

a x^{2} + b x + 7 = k (3 x^{2} - 2 x + 1)

拡張

k (3 x^{2} - 2 x + 1) : 3 k x^{2} - 2 k x + k

a x^{2} + b x + 7 = 3 k x^{2} - 2 k x + k

両辺から

- 2 k x + k

を引く

a x^{2} + b x + 7 - (- 2 k x + k) = 3 k x^{2} - 2 k x + k - (- 2 k x + k)

簡素化

a x^{2} + b x + 7 + 2 k x - k = 3 k x^{2}

3 k x^{2}

を左側に移動します

a x^{2} + b x + 7 + 2 k x - k - 3 k x^{2} = 0

標準的な形式で書く

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

(a - 3 k) x^{2} + (b + 2 k) x + 7 - k = 0

解くとthe二次式

x_{1, 2} = \frac{- ( b + 2 k ) \pm ( b + 2 k ) ^{2} - 4 ( a - 3 k ) ( 7 - k )}{2 ( a - 3 k )}

簡素化

(b + 2 k)^{2} - 4 (a - 3 k) (7 - k) : - 8 k^{2} + 4 ak + 4 bk + 84 k - 28 a + b^{2}

x_{1, 2} = \frac{- ( b + 2 k ) \pm - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}; k \neq = \frac{a}{3}

解を分離する

x_{1} = \frac{- ( b + 2 k ) + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}, x_{2} = \frac{- ( b + 2 k ) - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}

x = \frac{- ( b + 2 k ) + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )} : \frac{- b - 2 k + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}

x = \frac{- ( b + 2 k ) - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )} : \frac{- b - 2 k - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}

二次equationの解:

x = \frac{- b - 2 k + - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}, x = \frac{- b - 2 k - - 8 k ^{2} + 4 ak + 4 bk + 84 k - 28 a + b ^{2}}{2 ( a - 3 k )}; k \neq = \frac{a}{3}

グラフ

人気の例

((3x)^2+(4x)^2)-4x+975x=5x^2

((3 x)^{2} + (4 x)^{2}) - 4 x + 975 x = 5 x^{2}

x^2-2(k-1)x+6k-11=0

x^{2} - 2 (k - 1) x + 6 k - 11 = 0

a^{2} + 2 1^{2} = 2 9^{2}

6 x^{2} + 8 x - 4 = 0

π x^{2} = 500