Question

Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations `u+2y+3w=6,4u+5y+6w=12` and `6u+9v=4`. Further consider the expressions
`f(x)=(1/u+1/v+1/w)x^(2)+[(b-c)^(2)+(c-a)^(2)+(x-b)^(2)]`
`x+u+v+w=0` and `g(x)=20x^(2)+10(a-d)^(2)x-9=0`
`(u+v+w)` is equal to
A. `2`
B. `1/2`
C. `20`
D. `1/20`

Answer 1

Now `u+2v+3w=6`…….i
`4u+5v+6w=12`……..ii
and `6u+9v=4`……….iii
From Eqs I and ii we get
`2u+v=0` ……iv
Solving eqs iii and iv we get
`u=-1/3,v=2/3`
Now from Eq i we get `w=5/3`
`:.v+u+2w=-1/3+2/3+5/3=2`