One way to go is via complex numbers.
Hint: Take z1 = x + ia, z2 = y + ib, z3 = z+ic
And use the fact that
|z1 z2 z3| = |z1| |z2| |z3|
Express (x^2+a^2)(y^2+b^2)(z^2+c^2) as a sum of two squares
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4 Answers
kaymant
·2009-12-20 04:57:02
Lokesh Verma
·2009-12-21 07:22:21
yup exactly...
And this is what i wanted the users to think like.. but alas ;)
Hari Shankar
·2009-12-29 05:01:43
Also useful is Lagrange's Identity:
(a^2+b^2)(c^2+d^2) = (ac-bd)^2+(ad+bc)^2