Determine all possible triplets of nonzero perfect squares
(A, B, C) that satisfy this equation:
1 2 3 2
--- + --- + --- = ---
A B C 3
Prove that there are no others.
(In reply to Do i err ??
by Ady TZIDON)
Indeed, 9,9,9 does seem the only solution, as verified by
For totab = 2 To 10000
For a = 1 To totab -1
b = totab - a
a2 = a * a: b2 = b * b
num = 9 * a2 * b2
den = -(6 * a2 + 3 * b2 - 2 * a2 * b2)
If den > 0 Then
c2 = num / den
If c2 = Int(c2) And c2 > 0 Then
c = Int(Sqr(c2) + 0.5)
If c * c = c2 Then
Text1.Text = Text1.Text & Str(a2) & Str(b2) & Str(c2) & crlf
for sqrt(a) + sqrt(b) having values all the way up to ten thousand.
Posted by Charlie
on 2014-05-28 13:34:18