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Math is radical (Posted on 2019-03-19) Difficulty: 3 of 5
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.)
Some Thoughts 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               LHS
33 105 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
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