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人気のある代数 >

solvefor x,p^2+x^2+(p^2-q^2)x-q^2=0

解

解く

x, p^{2} + x^{2} + (p^{2} - q^{2}) x - q^{2} = 0

解

x = \frac{- p ^{2} + q ^{2} + ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2}, x = \frac{- p ^{2} + q ^{2} - ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2}

解答ステップ

p^{2} + x^{2} + (p^{2} - q^{2}) x - q^{2} = 0

標準的な形式で書く

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

x^{2} + (p^{2} - q^{2}) x + p^{2} - q^{2} = 0

解くとthe二次式

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

簡素化

(p^{2} - q^{2})^{2} - 4 \cdot 1 \cdot (p^{2} - q^{2}) : (p^{2} - q^{2})^{2} - 4 (p^{2} - q^{2})

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

解を分離する

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

x = \frac{- ( p ^{2} - q ^{2} ) + ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2 \cdot 1} : \frac{- p ^{2} + q ^{2} + ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2}

x = \frac{- ( p ^{2} - q ^{2} ) - ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2 \cdot 1} : \frac{- p ^{2} + q ^{2} - ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2}

二次equationの解:

x = \frac{- p ^{2} + q ^{2} + ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2}, x = \frac{- p ^{2} + q ^{2} - ( p ^{2} - q ^{2} ) ^{2} - 4 ( p ^{2} - q ^{2} )}{2}

グラフ

人気の例

6 + x = x^{2}

solvefor x,2x^2+a*y^2-3x+2y-1=0

so l v e f or x, 2 x^{2} + a \cdot y^{2} - 3 x + 2 y - 1 = 0

\frac{x}{2} = x^{2}

solvefor x,12=-1/2 x(x-r)

so l v e f or x, 12 = - \frac{1}{2} x (x - r)

(5x^2)/6 = 40/3

\frac{5 x ^{2}}{6} = \frac{40}{3}