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

解答

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

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

求解步骤

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

整理后得

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

使用求根公式求解

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

化简

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

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

将解分隔开

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

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

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

二次方程组的解是:

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

so l v e f or x, p (x + 1) = x^{2} + p

so l v e f or a, u = 50 a - 0.5 a^{2} + 60 m - 0.25 m^{2}

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

(\frac{3}{5} x - \frac{2}{3})^{2} = \frac{5}{6}

so l v e f or u, 1 + d^{2} u^{2} = (1 + \frac{d ^{2}}{2})^{2}