4x^2-4a^2x-b^4+a^4=0

解

4 x^{2} - 4 a^{2} x - b^{4} + a^{4} = 0

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

解答ステップ

4 x^{2} - 4 a^{2} x - b^{4} + a^{4} = 0

解くとthe二次式

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

簡素化

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

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

解を分離する

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

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

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

二次equationの解:

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