 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Math is radical (Posted on 2019-03-19) Consider the following equation
1+√2+√3+√6 = √(a+√(b+√(c+√d)))
where a, b, c, d are integers. Find these integers.

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 5.0000 (1 votes) Comments: ( Back to comment list | You must be logged in to post comments.) computer attempt is close but no cigar | Comment 1 of 2
goal = 1 + Sqr(2) + Sqr(3) + Sqr(6)

For d = 0 To 1000
srd = Sqr(d)
For c = -Int(srd) To 111
sr3 = Sqr(c + srd)
For b = -Int(sr3) To 111
sr2 = Sqr(sr3 + b)
For a = -Int(sr2) To 50
sr = Sqr(sr2 + a)
rat = sr / goal
If Abs(rat - 1) <= 0.000000001 Then
Text1.Text = Text1.Text & a & Str(b) & Str(c) & Str(d) & "     " & sr & Str(goal) & crlf
End If
DoEvents
Next
Next
Next
Next

finds only the following as the closest match:

` a  b   c  d           RHS               LHS33 105 17 131     6.59575411292311 6.59575411272515`

and it's not just rounding error; UBASIC confirms this precision's accuracy.

 Posted by Charlie on 2019-03-19 15:00:51 Please log in:

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