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人気のある代数 >

x^2+((a+1)/a)x+1=0

解

x^{2} + (\frac{a + 1}{a}) x + 1 = 0

解

x = \frac{- a - 1 + 2 a + 1 - 3 a ^{2}}{2 a}, x = \frac{- a - 1 - 2 a + 1 - 3 a ^{2}}{2 a}

解答ステップ

x^{2} + (\frac{a + 1}{a}) x + 1 = 0

拡張

x^{2} + (\frac{a + 1}{a}) x + 1 : x^{2} + x + \frac{x}{a} + 1

x^{2} + x + \frac{x}{a} + 1 = 0

標準的な形式で書く

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

x^{2} + (1 + \frac{1}{a}) x + 1 = 0

解くとthe二次式

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

簡素化

(1 + \frac{1}{a})^{2} - 4 \cdot 1 \cdot 1 : \frac{2 a + 1 - 3 a ^{2}}{a}

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

解を分離する

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

x = \frac{- ( 1 + \frac{1}{a} ) + \frac{2 a + 1 - 3 a ^{2}}{a}}{2 \cdot 1} : \frac{- a - 1 + 2 a + 1 - 3 a ^{2}}{2 a}

x = \frac{- ( 1 + \frac{1}{a} ) - \frac{2 a + 1 - 3 a ^{2}}{a}}{2 \cdot 1} : \frac{- a - 1 - 2 a + 1 - 3 a ^{2}}{2 a}

二次equationの解:

x = \frac{- a - 1 + 2 a + 1 - 3 a ^{2}}{2 a}, x = \frac{- a - 1 - 2 a + 1 - 3 a ^{2}}{2 a}

グラフ

人気の例

x^{2} + 8 x - 1920 = 0

solvefor y,y^2=x^5(2a-x)

so l v e f or y, y^{2} = x^{5} (2 a - x)

solvefor x,p*x^2-(3p+2)*x+(5p-2)=0

so l v e f or x, p \cdot x^{2} - (3 p + 2) \cdot x + (5 p - 2) = 0

solvefor x,y^3-7y-6y=e^2x(1+x)

so l v e f or x, y^{3} - 7 y - 6 y = e^{2} x (1 + x)

solvefor b,a=b(b+2a)

so l v e f or b, a = b (b + 2 a)