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受欢迎的代数 >

solvefor x,3x^2+4y^2-6x-24y+39=0

解答

求解

x, 3 x^{2} + 4 y^{2} - 6 x - 24 y + 39 = 0

解答

x = 1 + i \frac{3 ( - 6 + 2 y )}{3}, x = 1 + i \frac{3 ( 6 - 2 y )}{3}

求解步骤

3 x^{2} + 4 y^{2} - 6 x - 24 y + 39 = 0

改写成标准形式

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

3 x^{2} - 6 x + 4 y^{2} - 24 y + 39 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 ( 4 y ^{2} - 24 y + 39 )}{2 \cdot 3}

化简

(- 6)^{2} - 4 \cdot 3 (4 y^{2} - 24 y + 39) : i (- 123 + 43 y)

x_{1, 2} = \frac{- ( - 6 ) \pm i ( - 12 3 + 4 3 y )}{2 \cdot 3}

将解分隔开

x_{1} = \frac{- ( - 6 ) + i ( - 12 3 + 4 3 y )}{2 \cdot 3}, x_{2} = \frac{- ( - 6 ) - i ( - 12 3 + 4 3 y )}{2 \cdot 3}

x = \frac{- ( - 6 ) + i ( - 12 3 + 4 3 y )}{2 \cdot 3} : 1 + i \frac{3 ( - 6 + 2 y )}{3}

x = \frac{- ( - 6 ) - i ( - 12 3 + 4 3 y )}{2 \cdot 3} : 1 + i \frac{3 ( 6 - 2 y )}{3}

二次方程组的解是:

x = 1 + i \frac{3 ( - 6 + 2 y )}{3}, x = 1 + i \frac{3 ( 6 - 2 y )}{3}

作图

流行的例子

solvefor x,x^2+2x+y^2-6y=c

so l v e f or x, x^{2} + 2 x + y^{2} - 6 y = c

completesquare Ax^2+Dx

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

3^{2} + 4^{2} = r^{2}

5 x^{2} - 10 x + 7 = 0

solvefor x,21x^2+6xy+13y^2-114x+34y+73=0

so l v e f or x, 21 x^{2} + 6 x y + 13 y^{2} - 114 x + 34 y + 73 = 0