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受欢迎的代数 >

solvefor x,x^2+y^2+2x+1=0

解答

求解

x, x^{2} + y^{2} + 2 x + 1 = 0

解答

x = - 1 + i y, x = - i y - 1

求解步骤

x^{2} + y^{2} + 2 x + 1 = 0

改写成标准形式

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

x^{2} + 2 x + y^{2} + 1 = 0

使用求根公式求解

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

化简

2^{2} - 4 \cdot 1 \cdot (y^{2} + 1) : 2 i y

x_{1, 2} = \frac{- 2 \pm 2 i y}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- 2 + 2 i y}{2 \cdot 1}, x_{2} = \frac{- 2 - 2 i y}{2 \cdot 1}

x = \frac{- 2 + 2 i y}{2 \cdot 1} : - 1 + i y

x = \frac{- 2 - 2 i y}{2 \cdot 1} : - i y - 1

二次方程组的解是:

x = - 1 + i y, x = - i y - 1

作图

流行的例子

solvefor x,2x^2-4x-1=0

so l v e f or x, 2 x^{2} - 4 x - 1 = 0

\frac{x ^{2} + 10}{2} = 19

completesquare x^2-10x-4

co m pl e t es q u a re x^{2} - 10 x - 4

completesquare 2x^2+5x+3

co m pl e t es q u a re 2 x^{2} + 5 x + 3

solvefor x,x^2+xy+2y^2=18

so l v e f or x, x^{2} + x y + 2 y^{2} = 18