64x^2-(16a+4b)x+ab=0

解

64 x^{2} - (16 a + 4 b) x + ab = 0

x = \frac{a}{4}, x = \frac{b}{16}

解答ステップ

64 x^{2} - (16 a + 4 b) x + ab = 0

解くとthe二次式

x_{1, 2} = \frac{- ( - 16 a - 4 b ) \pm ( - 16 a - 4 b ) ^{2} - 4 \cdot 64 ab}{2 \cdot 64}

簡素化

(- 16 a - 4 b)^{2} - 4 \cdot 64 ab : 4 (4 a - b)

x_{1, 2} = \frac{- ( - 16 a - 4 b ) \pm 4 ( 4 a - b )}{2 \cdot 64}

解を分離する

x_{1} = \frac{- ( - 16 a - 4 b ) + 4 ( 4 a - b )}{2 \cdot 64}, x_{2} = \frac{- ( - 16 a - 4 b ) - 4 ( 4 a - b )}{2 \cdot 64}

x = \frac{- ( - 16 a - 4 b ) + 4 ( 4 a - b )}{2 \cdot 64} : \frac{a}{4}

x = \frac{- ( - 16 a - 4 b ) - 4 ( 4 a - b )}{2 \cdot 64} : \frac{b}{16}

二次equationの解:

x = \frac{a}{4}, x = \frac{b}{16}