Quadratic Equations

Let a,b,c,d be real nos. in G.P. If u,v,w satisfy the equations :

u+2v+3w=6
4u+5v+6w=12
6u+9v=4

then show that the roots of the equation

(1u+1v+1w)x² + [(b-c)² + (c-a)² + (d-b)²]x + u+v+w = 0

and 20x² + 10(a-d)²x - 9 = 0 are reciprocals of each other.

2 Answers

what is f??

The Eqn 1 (the one including u ,v , w) is reduced to

-9 / 10 x² + (a - d)² x + 2 = 0

[ Using b² = ac , c² = bd & bc = ad ]

Now, substitute 1/x in place of x to prove that the roots of eqn 2 r reciprocals of that of 1

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