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受欢迎的代数 >

solvefor x,x^2+y^2+z^2+8x-6y-4z-7=0

解答

求解

x, x^{2} + y^{2} + z^{2} + 8 x - 6 y - 4 z - 7 = 0

解答

x = - 4 + - y^{2} + 6 y + 4 z + 23 - z^{2}, x = - - y^{2} + 6 y + 4 z + 23 - z^{2} - 4

求解步骤

x^{2} + y^{2} + z^{2} + 8 x - 6 y - 4 z - 7 = 0

改写成标准形式

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

x^{2} + 8 x + y^{2} + z^{2} - 6 y - 4 z - 7 = 0

使用求根公式求解

x_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 1 \cdot ( y ^{2} + z ^{2} - 6 y - 4 z - 7 )}{2 \cdot 1}

化简

8^{2} - 4 \cdot 1 \cdot (y^{2} + z^{2} - 6 y - 4 z - 7) : 2 - y^{2} + 6 y + 4 z + 23 - z^{2}

x_{1, 2} = \frac{- 8 \pm 2 - y ^{2} + 6 y + 4 z + 23 - z ^{2}}{2 \cdot 1}

将解分隔开

x_{1} = \frac{- 8 + 2 - y ^{2} + 6 y + 4 z + 23 - z ^{2}}{2 \cdot 1}, x_{2} = \frac{- 8 - 2 - y ^{2} + 6 y + 4 z + 23 - z ^{2}}{2 \cdot 1}

x = \frac{- 8 + 2 - y ^{2} + 6 y + 4 z + 23 - z ^{2}}{2 \cdot 1} : - 4 + - y^{2} + 6 y + 4 z + 23 - z^{2}

x = \frac{- 8 - 2 - y ^{2} + 6 y + 4 z + 23 - z ^{2}}{2 \cdot 1} : - - y^{2} + 6 y + 4 z + 23 - z^{2} - 4

二次方程组的解是:

x = - 4 + - y^{2} + 6 y + 4 z + 23 - z^{2}, x = - - y^{2} + 6 y + 4 z + 23 - z^{2} - 4

作图

流行的例子

\frac{8}{3} = 4 - x^{2}

(x-2)2+x(x+1)=24

(x - 2) 2 + x (x + 1) = 24

x^{2} + 8 x - 32 = 0

solvefor z,x^3z^2-5xy^5z=x^2+y^3

so l v e f or z, x^{3} z^{2} - 5 x y^{5} z = x^{2} + y^{3}

5x^2-x+6=5-7x-4x^2

5 x^{2} - x + 6 = 5 - 7 x - 4 x^{2}