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受欢迎的代数 >

solvefor x,f(x+1)=3(x+1)^2+1

解答

求解

x, f (x + 1) = 3 (x + 1)^{2} + 1

解答

x = \frac{- 6 + f + f ^{2} - 12}{6}, x = \frac{- 6 + f - f ^{2} - 12}{6}

求解步骤

f (x + 1) = 3 (x + 1)^{2} + 1

展开

f (x + 1) : x f + f

展开

3 (x + 1)^{2} + 1 : 3 x^{2} + 6 x + 4

x f + f = 3 x^{2} + 6 x + 4

交换两边

3 x^{2} + 6 x + 4 = x f + f

将

f

para o lado esquerdo

3 x^{2} + 6 x + 4 - f = x f

将

x f

para o lado esquerdo

3 x^{2} + 6 x + 4 - f - x f = 0

改写成标准形式

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

3 x^{2} + (6 - f) x + 4 - f = 0

使用求根公式求解

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

化简

(6 - f)^{2} - 4 \cdot 3 (4 - f) : f^{2} - 12

x_{1, 2} = \frac{- ( 6 - f ) \pm f ^{2} - 12}{2 \cdot 3}

将解分隔开

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

x = \frac{- ( 6 - f ) + f ^{2} - 12}{2 \cdot 3} : \frac{- 6 + f + f ^{2} - 12}{6}

x = \frac{- ( 6 - f ) - f ^{2} - 12}{2 \cdot 3} : \frac{- 6 + f - f ^{2} - 12}{6}

二次方程组的解是:

x = \frac{- 6 + f + f ^{2} - 12}{6}, x = \frac{- 6 + f - f ^{2} - 12}{6}

作图

流行的例子

(2 x - 3)^{2} = 5

- 3 x^{2} + 3 x + 1 = 0

7^{2} + x^{2} = 1 3^{2}

p^2+0.8p+0.16=1

p^{2} + 0.8 p + 0.16 = 1

(x+4)^2+(x-3)^2=(x-5)^2

(x + 4)^{2} + (x - 3)^{2} = (x - 5)^{2}