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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: 3.0000 (2 votes)

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computer attempt is close but no cigar

| Comment 1 of 3

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

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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