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人気のある代数 >

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

解

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

解

x = \frac{2 a ^{2} + 2 b ^{2} + ( - 2 a ^{2} - 2 b ^{2} ) ^{2} - 4 ( a ^{2} - b ^{2} )}{2}, x = \frac{2 a ^{2} + 2 b ^{2} - ( - 2 a ^{2} - 2 b ^{2} ) ^{2} - 4 ( a ^{2} - b ^{2} )}{2}

解答ステップ

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

拡張

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

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

標準的な形式で書く

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

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

解くとthe二次式

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

簡素化

(- 2 a^{2} - 2 b^{2})^{2} - 4 \cdot 1 \cdot (a^{2} - b^{2}) : (- 2 a^{2} - 2 b^{2})^{2} - 4 (a^{2} - b^{2})

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

解を分離する

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

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

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

二次equationの解:

x = \frac{2 a ^{2} + 2 b ^{2} + ( - 2 a ^{2} - 2 b ^{2} ) ^{2} - 4 ( a ^{2} - b ^{2} )}{2}, x = \frac{2 a ^{2} + 2 b ^{2} - ( - 2 a ^{2} - 2 b ^{2} ) ^{2} - 4 ( a ^{2} - b ^{2} )}{2}

グラフ

人気の例

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

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

5/2*x+2/3*x= 95/2*x^2

\frac{5}{2} \cdot x + \frac{2}{3} \cdot x = \frac{95}{2} \cdot x^{2}

solvefor x,4x^2-4xy+y^2-4x-8y-20=0

so l v e f or x, 4 x^{2} - 4 x y + y^{2} - 4 x - 8 y - 20 = 0

v^{1} c^{1} = v^{2} c^{2}

2x^2-5x+2=0,x-2<0

2 x^{2} - 5 x + 2 = 0, x - 2 < 0