If every pair from among the equations `x^2+a x+b c=0. x^2+b x+c a=0,a n dx 62+c x+a b=0` has a common root, then the sum of the three common roots is `-1//2(a+b+c)` the sum of the three common roots is `2(a+b+c)` the product of the three common roots is `a b c` the product of the three common roots is `a^2b^2c^2`

Explanation

`(18x^(2)+12x+4)^(n) = 2^(n)[2+9x^(2)+6x]^(n)`
Now, `a_(r )` is coefficient of `x^(r )` in `2^(n) [(3x+1)^(2)+1]^(n)`. Hence
`a_(r) =` Coefficient of `x^(r )2^(n)[.^(n)C_(0)(3x+1)^(2n)+.^(n)C_(1)(3x+1)^(2n-2) + .^(n)C_(2)(3x+1)^(2n-4)+"…."+.^(n)C_(r )(3x+1)^(2n-2r)+"....."]`
or `a_(r)=2^(n)[.^(n)C_(0)3^(r).^(2n)C_(r)+.^(n)C_(1)3^(r).^(2n-2)C_(r)+.^(n)C_(2)3^(r).^(2n-4)C_(r)+"...."]`
`= 2^(n)3^(r)[.^(n)C_(0).^(2n)C_(r)+.^(n)C_(1).^(2n-2)C_(r)+.^(n)C_(2).^(2n-4)C_(r)+"...."]`