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受欢迎的代数 >

solvefor x,[3p+1]x^2+2[p+1]x+p=0

解答

求解

x, [3 p + 1] \cdot x^{2} + 2 [p + 1] \cdot x + p = 0

解答

x = \frac{- p - 1 + - 2 p ^{2} + p + 1}{3 p + 1}, x = - \frac{p + - 2 p ^{2} + p + 1 + 1}{3 p + 1}; p \neq = - \frac{1}{3}

求解步骤

[3 p + 1] x^{2} + 2 [p + 1] x + p = 0

展开

(3 p + 1) x^{2} + 2 (p + 1) x + p : 3 x^{2} p + x^{2} + 2 x p + 2 x + p

3 x^{2} p + x^{2} + 2 x p + 2 x + p = 0

改写成标准形式

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

(3 p + 1) x^{2} + (2 p + 2) x + p = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 2 p + 2 ) \pm ( 2 p + 2 ) ^{2} - 4 ( 3 p + 1 ) p}{2 ( 3 p + 1 )}

化简

(2 p + 2)^{2} - 4 (3 p + 1) p : 2 - 2 p^{2} + p + 1

x_{1, 2} = \frac{- ( 2 p + 2 ) \pm 2 - 2 p ^{2} + p + 1}{2 ( 3 p + 1 )}; p \neq = - \frac{1}{3}

将解分隔开

x_{1} = \frac{- ( 2 p + 2 ) + 2 - 2 p ^{2} + p + 1}{2 ( 3 p + 1 )}, x_{2} = \frac{- ( 2 p + 2 ) - 2 - 2 p ^{2} + p + 1}{2 ( 3 p + 1 )}

x = \frac{- ( 2 p + 2 ) + 2 - 2 p ^{2} + p + 1}{2 ( 3 p + 1 )} : \frac{- p - 1 + - 2 p ^{2} + p + 1}{3 p + 1}

x = \frac{- ( 2 p + 2 ) - 2 - 2 p ^{2} + p + 1}{2 ( 3 p + 1 )} : - \frac{p + - 2 p ^{2} + p + 1 + 1}{3 p + 1}

二次方程组的解是:

x = \frac{- p - 1 + - 2 p ^{2} + p + 1}{3 p + 1}, x = - \frac{p + - 2 p ^{2} + p + 1 + 1}{3 p + 1}; p \neq = - \frac{1}{3}

作图

流行的例子

m/n*x^2+n/m =1-2x

\frac{m}{n} \cdot x^{2} + \frac{n}{m} = 1 - 2 x

e = d^{2} \cdot 10 + d^{1}

solvefor y,x^3+y^2-27x-10y+30=0

so l v e f or y, x^{3} + y^{2} - 27 x - 10 y + 30 = 0

(x-4)^2-1=-0.75

(x - 4)^{2} - 1 = - 0.75

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