已知 ae = 89.21, be =102.87, ce = 84.35, a.x = 0, a.y = 0, a.z = 0, b.x = 0, b.y = 20, b.z = 0, c.x = 100, c.y = 20, c.z = 10, 求解
Math.pow(x - a.x, 2) + Math.pow(y - a.y, 2) + Math.pow(z - a.z, 2) - ae * ae;
Math.pow(x - b.x, 2) + Math.pow(y - b.y, 2) + Math.pow(z - b.z, 2) - be * be;
Math.pow(x - c.x, 2) + Math.pow(y - c.y, 2) + Math.pow(z - c.z, 2) - ce * ce; 
方程组

给定以下方程组：

1. \(\text{Equation 1: } (x - a_x)^2 + (y - a_y)^2 + (z - a_z)^2 = ae^2\)
2. \(\text{Equation 2: } (x - b_x)^2 + (y - b_y)^2 + (z - b_z)^2 = be^2\)
3. \(\text{Equation 3: } (x - c_x)^2 + (y - c_y)^2 + (z - c_z)^2 = ce^2\)

代入已知条件：
- \(a_x = 0\), \(a_y = 0\), \(a_z = 0\)
- \(b_x = 0\), \(b_y = 20\), \(b_z = 0\)
- \(c_x = 100\), \(c_y = 20\), \(c_z = 10\)
- \(ae = 89.21\)
- \(be = 102.87\)
- \(ce = 84.35\)

可以将方程简化为：

1. \(\text{Equation 1: } x^2 + y^2 + z^2 = 89.21^2\)
2. \(\text{Equation 2: } x^2 + (y - 20)^2 + z^2 = 102.87^2\)
3. \(\text{Equation 3: } (x - 100)^2 + (y - 20)^2 + (z - 10)^2 = 84.35^2\)

我们将通过解这个方程组来找到 \(x\), \(y\), 和 \(z\) 的值。

### 第一步：解方程1与方程2

首先，我们用方程1减去方程2：

\[
x^2 + y^2 + z^2 - \left[x^2 + (y - 20)^2 + z^2\right] = 89.21^2 - 102.87^2
\]

展开并简化：

\[
y^2 - \left[(y - 20)^2\right] = 89.21^2 - 102.87^2
\]

\[
y^2 - (y^2 - 40y + 400) = 89.21^2 - 102.87^2
\]

\[
40y - 400 = 89.21^2 - 102.87^2
\]

计算右边的数值：

\[
40y = 89.21^2 - 102.87^2 + 400
\]

\[
y = \frac{89.21^2 - 102.87^2 + 400}{40}
\]

计算得到 \(y\) 的数值。

### 第二步：解方程1与方程3

用方程1减去方程3：

\[
x^2 + y^2 + z^2 - \left[(x - 100)^2 + (y - 20)^2 + (z - 10)^2\right] = 89.21^2 - 84.35^2
\]

展开并简化得到关于 \(x\), \(y\), \(z\) 的方程。

### 第三步：求解 \(x\), \(y\), \(z\)

通过代入法或其他适当的解法，解方程组，最终得到 \(x\), \(y\), \(z\) 的具体值。

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