Let a, b, c, d be real numbers in G. P. If u, v, w, satisfy the system of equations u + 2v + 3w = 64u + 5v + 6w = 126u + 9v = 4Then show that the roots of the equations(1/u + 1/v + 1/w)x2 + [(b-c)2 + (c – a)2 + (d – b)2] x + u + v + w = 0And 20x2 + 10(a- d)2 x – 9 = 0 are reciprocals of each other.
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
6u + 9v = 4
Then show that the roots of the equations
(1/u + 1/v + 1/w)x2 + [(b-c)2 + (c – a)2 + (d – b)2] x + u + v + w = 0
And 20x2 + 10(a- d)2 x – 9 = 0 are reciprocals of each other.
Simran Bhatia , 10 Years ago
Grade 11
