標題: [發問] EXCEL VBA求一元二次方程式 (不用公式解) [打印本頁]

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作者: 森野    時間: 2021-10-18 09:50     標題: EXCEL VBA求一元二次方程式 (不用公式解)

本帖最後由 森野 於 2021-10-18 09:52 編輯

一元二次方程式:X²+2X-4=0 ,用公式解x=(-b±√b^2-4ac)/2a的方式，可以求出X1=1.23606797749979 X2=-3.2360679774997
藉此可知X1位於1~2之間 X2位於-3~-4之間  如果不用公式解的方式 要如何讓電腦判別X1、X2是位於1~2及-3~-4之間 之間 並且算到X1=1.2360679774997，X2=-3.2360679774997
邏輯的部分就是如果沒有公式，以電腦的邏輯，判別方程式的走向，找出接近的解答並加以修正誤差值，想知道如何設定程式碼以及詳細說明

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作者: Andy2483    時間: 2021-10-19 11:12

本帖最後由 Andy2483 於 2021-10-19 11:22 編輯

回復 1# 森野


    Sub 一元二次方程式求解()
Workbooks.Add
[MM:MM].Interior.ColorIndex = 1
[601:601].Interior.ColorIndex = 1
ActiveWindow.Zoom = 10
Cells.RowHeight = 6
Cells.ColumnWidth = 0.5
Dim X, Y, X1, X2, Xn1, Xn2, a, b, c
Y = a * X ^ 2 + b * X + c
a = 1
b = 2
c = -4
X1 = (-b + (b ^ 2 - 4 * a * (c)) ^ 0.5) / (2 * a) '<<<
X2 = (-b - (b ^ 2 - 4 * a * (c)) ^ 0.5) / (2 * a) '<<<
MsgBox "X1 = " & X1 & vbLf & vbLf & "X2 = " & X2
Cells(601, X1 * 100 + 351).Interior.ColorIndex = 3
Cells(601, X2 * 100 + 351).Interior.ColorIndex = 3
For X = 1.4 To -3.4 Step -0.01
   Y = Round(a * X ^ 2 + b * X + c, 2)
   Cells(601 + Y * 100, X * 100 + 351).Interior.ColorIndex = 3
Next
End Sub

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作者: Andy2483    時間: 2021-10-20 16:45

更正:拋物線開口朝上
Option Explicit
Sub TEST()
Cells.Interior.ColorIndex = xlNone
Dim X, Y, a, b, c, n, U1, U2, u, v, S, S0, S1, Y0, Y1, X1, X2, P, J, B2_4AC
J = 1
Y = a * X ^ n + b * X + c:  a = 1: b = 2: c = -4: n = 2
B2_4AC = b ^ 2 - 4 * a * c
If n = 2 Then
   If (4 * a * c - b ^ 2) / 4 * a = 0 Then
      MsgBox "唯一解 X= " & (-b) / (2 * a): Exit Sub
      ElseIf ((4 * a * c - b ^ 2) / 4 * a > 0 And a > 0) Or ((4 * a * c - b ^ 2) / 4 * a < 0 And a < 0) Then
         MsgBox " X 無解!": Exit Sub
   End If
   If b = 0 And c < 0 Then X1 = (-c / a) ^ 0.5: X2 = -(-c / a) ^ 0.5
   If a > 0 Then MsgBox "拋物線開口向上" Else: MsgBox "拋物線開口向下"
End If
U1 = Round((-b - B2_4AC ^ 0.5) / (2 * a), 2)
U2 = Round((-b + B2_4AC ^ 0.5) / (2 * a), 2)
u = (Abs(U1) + 1) * 110: v = (Abs(c) + 1) * 110
Columns(u).Interior.ColorIndex = 1
Rows(v).Interior.ColorIndex = 1
Cells(v, u - Abs(U1) * 100).Interior.ColorIndex = 3
Cells(v, Abs(U2) * 100 + u).Interior.ColorIndex = 3
For X = U1 - 0.2 To U2 + 0.2 Step 0.01
   Y = Round(a * X ^ 2 + b * X + c, 2)
   Cells(v - Y * 100, X * 100 + u).Interior.ColorIndex = 3
Next
888: S0 = -100 * J: S1 = 100 * J: S = J: P = 1
999
For X = S0 To S1 Step S
   Y0 = a * X ^ n + b * X + c
   Y1 = (a * (X + S)) ^ n + (b * (X + S)) + c
   P = Y0 * Y1
   If (S < 10 ^ -13 And J = 1) Or (S > -(10 ^ -13) And J = -1) Then P = 0
   If P = 0 Then
      If c = 0 And J = 1 Then MsgBox "X1= " & X
      If c = 0 And J = -1 Then MsgBox "X2= " & X
      If J = -1 Then: MsgBox "X1= " & X1 & vbLf & vbLf & "X2= " & X2: Exit Sub
      J = -1: GoTo 888
      ElseIf P < 0 Then
         S0 = X: S1 = S0 + S: S = S / 10  '
         If J = 1 Then
            MsgBox "X1 介於 " & S0 & " ~ " & S1
            X1 = S1
            Else
               MsgBox "X2 介於 " & S0 & " ~ " & S1
               X2 = S1
         End If
         GoTo 999
   End If
Next
End Sub

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