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人気のある代数 >

(x-m)(x-n)=k^2

解

(x - m) (x - n) = k^{2}

解

x = \frac{n + m + m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2}, x = \frac{n + m - m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2}

解答ステップ

(x - m) (x - n) = k^{2}

拡張

(x - m) (x - n) : x^{2} - n x - m x + mn

x^{2} - n x - m x + mn = k^{2}

k^{2}

を左側に移動します

x^{2} - n x - m x + mn - k^{2} = 0

標準的な形式で書く

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

x^{2} - (n + m) x + mn - k^{2} = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - n - m ) \pm ( - n - m ) ^{2} - 4 \cdot 1 \cdot ( mn - k ^{2} )}{2 \cdot 1}

簡素化

(- n - m)^{2} - 4 \cdot 1 \cdot (mn - k^{2}) : m^{2} - 2 mn + n^{2} + 4 k^{2}

x_{1, 2} = \frac{- ( - n - m ) \pm m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2 \cdot 1}

解を分離する

x_{1} = \frac{- ( - n - m ) + m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2 \cdot 1}, x_{2} = \frac{- ( - n - m ) - m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2 \cdot 1}

x = \frac{- ( - n - m ) + m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2 \cdot 1} : \frac{n + m + m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2}

x = \frac{- ( - n - m ) - m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2 \cdot 1} : \frac{n + m - m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2}

二次equationの解:

x = \frac{n + m + m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2}, x = \frac{n + m - m ^{2} - 2 mn + n ^{2} + 4 k ^{2}}{2}

グラフ

人気の例

x^{2} + 1 = 6 x

C=1600-10x+0.25x^2

C = 1600 - 10 x + 0.25 x^{2}

((3x+2)/4)^2=12

(\frac{3 x + 2}{4})^{2} = 12

x + 3 = 4 x^{2}

p^{2} + 6 p - 72 = 0