Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations `u+2v+3w=6,4u+5v+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

Options

A. `2`
B. `1/2`
C. `20`
D. `1/20`

Explanation

To solve the problem, we need to find the values of \( u \), \( v \), and \( w \) from the given system of equations, and then calculate \( u + v + w \).

### Step 1: Write down the equations

The system of equations is:
1. \( u + 2v + 3w = 6 \) (Equation 1)
2. \( 4u + 5v + 6w = 12 \) (Equation 2)
3. \( 6u + 9v = 4 \) (Equation 3)
...