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受欢迎的代数 >

solvefor x,f=x^2+6x-1f(x+h)-f((x))/h

解答

求解

x, f = x^{2} + 6 x - 1 f (x + h) - f \frac{( x )}{h}

解答

x = \frac{- 6 h + h f + f + h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{2 h}, x = \frac{- 6 h + h f + f - h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{2 h}

求解步骤

f = x^{2} + 6 x - 1 \cdot f (x + h) - f \frac{( x )}{h}

展开

x^{2} + 6 x - 1 \cdot f (x + h) - f \frac{x}{h} : x^{2} + 6 x - x f - h f - \frac{x f}{h}

f = x^{2} + 6 x - x f - h f - \frac{x f}{h}

交换两边

x^{2} + 6 x - x f - h f - \frac{x f}{h} = f

将

f

para o lado esquerdo

x^{2} + 6 x - x f - h f - \frac{x f}{h} - f = 0

改写成标准形式

a x^{2} + b x + c = 0

x^{2} + (6 - f - \frac{f}{h}) x - h f - f = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 6 - f - \frac{f}{h} ) \pm ( 6 - f - \frac{f}{h} ) ^{2} - 4 \cdot 1 \cdot ( - h f - f )}{2 \cdot 1}

化简

(6 - f - \frac{f}{h})^{2} - 4 \cdot 1 \cdot (- h f - f) : \frac{h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{h}

x_{1, 2} = \frac{- ( 6 - f - \frac{f}{h} ) \pm \frac{h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{h}}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- ( 6 - f - \frac{f}{h} ) + \frac{h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{h}}{2 \cdot 1}, x_{2} = \frac{- ( 6 - f - \frac{f}{h} ) - \frac{h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{h}}{2 \cdot 1}

x = \frac{- ( 6 - f - \frac{f}{h} ) + \frac{h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{h}}{2 \cdot 1} : \frac{- 6 h + h f + f + h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{2 h}

x = \frac{- ( 6 - f - \frac{f}{h} ) - \frac{h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{h}}{2 \cdot 1} : \frac{- 6 h + h f + f - h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{2 h}

二次方程组的解是:

x = \frac{- 6 h + h f + f + h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{2 h}, x = \frac{- 6 h + h f + f - h ^{2} f ^{2} + 4 h ^{3} f - 8 h ^{2} f + h ( 2 f ^{2} - 12 f ) + f ^{2} + 36 h ^{2}}{2 h}

作图

流行的例子

solvefor x,q^{561.3}x^2-22x+7=0

so l v e f or x, q^{561.3} x^{2} - 22 x + 7 = 0

solvefor x,5x^2+2y^2+4xy+4y-8x+14=0

so l v e f or x, 5 x^{2} + 2 y^{2} + 4 x y + 4 y - 8 x + 14 = 0

5 x - 5 x^{2} - 1.25 = 0

solvefor a,(99)^2=(a+b)^2

so l v e f or a, (99)^{2} = (a + b)^{2}

solvefor m,x^6+9x^4+24m^2+16=0

so l v e f or m, x^{6} + 9 x^{4} + 24 m^{2} + 16 = 0