Let a, b, c, d be real numbers in G.P. ...

Let `a, b, c, d` be real numbers in `G.P.` If `u, v, w` satisfy the system of equations `u + 2v +3w = 6,4u + 5v + 6w =12 and 6u + 9v = 4` then show that the roots of the equation `(1/u+1/v+1/w)x^2+[(b-c)^2+(c-a)^2+(d-b)^2]x+u+v+w=0` and '20x^2 +10(a-d)^2 x-9=0` are reciprocals of each other.

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