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EXCEL VBA求一元二次方程式 (不用公式解)(2)

本帖最後由 Andy2483 於 2021-10-20 14:32 編輯

回復 1# 森野


參考
Option Explicit
Sub TEST()
Dim X, Y, a, b, c, n, U1, U2, u, v, S, S0, S1, Y0, Y1, X1, X2, P, J
J = 1: Y = a * X ^ n + b * X + c: a = 1: b = 2: c = -4: n = 2
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
End If
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 X1 = X
      If c = 0 And J = -1 Then 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
End Sub

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本帖最後由 Andy2483 於 2021-10-21 08:56 編輯

回復 1# 森野


Option Explicit
Sub 一元二次方程式()
'X ^ 2 + 2 * X - 4 = 0 有兩解
Dim X, S, S0, S1, Y0, Y1, X1, X2, P
S0 = -1000
S1 = 1000
S = 1
'↑設定變數初值
888
'↓開始迴圈(-1000 到 1000 間隔1)
For X = S0 To S1 Step S
   Y0 = X ^ 2 + 2 * X - 4
   Y1 = (X + S) ^ 2 + 2 * (X + S) - 4
   P = Y0 * Y1
   '↓運用二次函數在Y值=0前的負數與Y值=0後的正數乘積是負數
   If P < 0 Then
      S0 = X '重新給S0設定值
      S1 = S0 + S '重新給S1設定值
      S = S / 10  '重新給S設定值
      MsgBox "X1 介於 " & S0 & " ~ " & S1
      X1 = S1
      GoTo 888 '結束迴圈,跳到 888 位置繼續執行
   End If
Next
''''''''''''''''''''''''''''''''''''''''''''''''
S0 = 1000
S1 = -1000
S = -1
'↑重設變數初值
999
'↓開始迴圈(1000 到 -1000 間隔-1)
For X = S0 To S1 Step S
   Y0 = X ^ 2 + 2 * X - 4
   Y1 = (X + S) ^ 2 + 2 * (X + S) - 4
   P = Y0 * Y1
   If P < 0 Then
      S0 = X
      S1 = S0 + S
      S = S / 10
      MsgBox "X2 介於 " & S0 & " ~ " & S1
      X2 = S1
      GoTo 999
   End If
Next
MsgBox "X1= " & X1 & vbLf & vbLf & "X2= " & X2
End Sub

Sub 一元二次方程式整數解1()
Dim X
For X = -1000 To 1000 Step 1
   If X ^ 2 - 4 = 0 Then MsgBox "X = " & X
Next
End Sub

Sub 一元二次方程式整數解2()
'1奈米(nm)= 10 埃(A)= 10^-9m
'電腦要RUN 2000*10^9次判斷,EXCEL會感覺當掉
Dim X
For X = -1000 To 1000 Step 10 ^ -9
   If X ^ 2 - 4 = 0 Then MsgBox "X = " & X
Next
End Sub

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回復 6# ML089


    前輩厲害!
前輩是資訊科系嗎?
我是機械科系,腦筋比較駑鈍,也老了才學VBA!
對前輩們非常佩服!
我們的MIS 該上這論壇來研究研究!
該用EXCEL當ERP的前台!
謝謝分享!

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回復 8# ML089


1.30年前機械系是學C語言,沒認真學!一支草一點露! 往3D Catia 鑽研到交棒,轉管理才發現管理不是罵罵人就好,一分證據說一分話才能服眾!
逆著學VBA,從錄製巨集開始學,一路沒競爭者又很雞婆到處幫同事寫堪用的巨集! 看到以前的 貴人在此論壇!欣喜就進來了!

2.老年痴呆症狀有點跡象了,視力也退化了!常動腦.常段練身體,保持健康才是最重要的!共勉

3.對二次曲線有興趣,就複習了 y=ax2+bx+c ,剛好版主要收斂得到解答的方法,也是一股腦用一招半式回答!
搜尋了Median找到這網頁: https://docs.microsoft.com/zh-tw/office/vba/api/excel.worksheetfunction.median
拋磚引玉學到了很多! 謝謝! 也謝謝論壇的多元性!

4.後輩用多次曲線的概念研究了一元四次方程式的實數解法也放上來! 記錄下來! 多年以後再回頭看此帖! 應該是五味雜陳!
請有興趣的前輩們分享.指導!謝謝!

Option Explicit
Sub 一元一二三四次方程式_實數解()
Dim InB$, Q$, i&, x#, x1#, a#, a1#, a2#, b#, c#, s#, S0#, S1#, S2#, Y0#, Y1#
Dim P#, J$, T&, d&, Arr, st#, S3#, K$, K1$, K2$, Kb$, Kc$
InB = UCase(InputBox("請輸入方程式 例:  X4-6X3+X2+2X+24=0", "請輸入", "2X4-4X3-3X2+7X-2=0"))
If (InB Like "*0" = False And InB Like "*#") Or InB Like "*X" Then InB = InB & "=0"
Q = InB: InB = Replace(InB, " ", "")
If InB Like "*X*=0" = False Or InB Like "*,*" Then T = -1: GoTo 777
If InB Like "X*" Then InB = "1" & InB
If InB Like "-X*" Then InB = "-1" & InB
InB = Replace(Replace(InB, "+X", "+1X"), "-X", "-1X")
InB = Replace(Replace(Replace(Replace(InB, "X4=", "X4+0="), _
      "X3=", "X3+0="), "X2=", "X2+0="), "X1=", "X1+0=")
InB = Replace(Replace(Replace(Replace(InB, "+", ",+"), "-", ",-"), "=0", ",=,"), "X", ",X")
Arr = Split(InB, ",")
If InStr(",X4,X3,X2,X,", "," & Arr(1) & ",") = 0 Then T = -3: GoTo 777
For i = 0 To UBound(Arr)
   If Arr(i) = "X4" Then a2 = Arr(i - 1)
   If Arr(i) = "X3" Then a1 = Arr(i - 1)
   If Arr(i) = "X2" Then a = Arr(i - 1)
   If Arr(i) = "X" Then b = Arr(i - 1)
   If Arr(i) = "=" Then c = Arr(i - 1)
Next
K = a: K1 = a1: K2 = a2: Kb = b: Kc = c:
If K & K1 & K2 & Kb & Kc Like "*0.*" Then T = -4: GoTo 777
T = 0: d = 26: S0 = -10001: S1 = 10001: S2 = S1: s = 0.5: st = s: P = 1
999
For x = S0 To S1 Step s
   DoEvents
   If s = st Then S3 = x
   Y0 = a2 * x ^ 4 + a1 * x ^ 3 + a * x ^ 2 + b * x + c: x1 = x + s
   Y1 = a2 * x1 ^ 4 + a1 * x1 ^ 3 + a * x1 ^ 2 + b * x1 + c
   If Y0 = 0 Then
      J = J & vbLf & "實數解X = " & x: S0 = S3 + s: S1 = S2: GoTo 999
   End If
   If Y1 = Y0 Then S0 = x + st: S1 = S2: GoTo 999
   P = Y0 * Y1
   If Int(Abs(P * 10 ^ d)) = 0 Then
      T = T + 1
      If s <> st Then J = J & vbLf & "實數解X = " & x1
      s = st: S0 = S3 + s: S1 = S2: GoTo 999
   End If
   If Int(Abs(s * 10 ^ d)) = 0 Then P = 0
   If P < 0 Then
      S0 = x: S1 = S0 + s: s = s / 10: GoTo 999
      ElseIf P > Abs(a2) + Abs(a1) + Abs(a) + Abs(b) + Abs(c) Then
         S0 = x + st: S1 = S2: GoTo 999
   End If
Next
777
If T > 0 Then
   MsgBox Q & vbLf & J
   ElseIf T = 0 Then
      MsgBox Q & vbLf & vbLf & " X 無實數解!"
   Else
      MsgBox Q & vbLf & vbLf & " 無法執行!"
End If
End Sub

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回復 11# ML089


    前輩教師節快樂
向您道歉 sorry:
10樓之後忙新的案件,好長一段時間沒上論壇學習,前幾天學習Function ()才看到11樓的前輩指導回覆,心�堣@直過意不去,趁今天教師節向前輩回覆,並祝前輩 教師節快樂

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