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

解

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

x = 3 a, x = 2 b

解答ステップ

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

解くとthe二次式

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

簡素化

(- 3 a - 2 b)^{2} - 4 \cdot 1 \cdot 6 ab : 3 a - 2 b

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

解を分離する

x_{1} = \frac{- ( - 3 a - 2 b ) + 3 a - 2 b}{2 \cdot 1}, x_{2} = \frac{- ( - 3 a - 2 b ) - ( 3 a - 2 b )}{2 \cdot 1}

x = \frac{- ( - 3 a - 2 b ) + 3 a - 2 b}{2 \cdot 1} : 3 a

x = \frac{- ( - 3 a - 2 b ) - ( 3 a - 2 b )}{2 \cdot 1} : 2 b

二次equationの解:

x = 3 a, x = 2 b