2abx^2-(b^2+6a^2)x+3ab=0

解

2 ab x^{2} - (b^{2} + 6 a^{2}) x + 3 ab = 0

x = \frac{3 a}{b}, x = \frac{b}{2 a}; 2 ab \neq = 0

解答ステップ

2 ab x^{2} - (b^{2} + 6 a^{2}) x + 3 ab = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - b ^{2} - 6 a ^{2} ) \pm ( - b ^{2} - 6 a ^{2} ) ^{2} - 4 \cdot 2 ab \cdot 3 ab}{2 \cdot 2 ab}

簡素化

(- b^{2} - 6 a^{2})^{2} - 4 \cdot 2 ab \cdot 3 ab : (6 a + b) (6 a - b)

x_{1, 2} = \frac{- ( - b ^{2} - 6 a ^{2} ) \pm ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab}; 2 ab \neq = 0

解を分離する

x_{1} = \frac{- ( - b ^{2} - 6 a ^{2} ) + ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab}, x_{2} = \frac{- ( - b ^{2} - 6 a ^{2} ) - ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab}

x = \frac{- ( - b ^{2} - 6 a ^{2} ) + ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab} : \frac{3 a}{b}

x = \frac{- ( - b ^{2} - 6 a ^{2} ) - ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab} : \frac{b}{2 a}

二次equationの解:

x = \frac{3 a}{b}, x = \frac{b}{2 a}; 2 ab \neq = 0