For what values of `m epsilonR`, both roots of the equation `x^(2)-6mx+9m^(2)-2m+2=0` exceed 3?

Explanation

Let `f(x)=x^(2)-6mx+9m^(2)-2m+2`
As both roots of `f(x)=0` are greater than 3, we can take `Dge0, af(3)gt0` and `-b/(2a)gt3`.
(i) Consiser `D ge0`
`(-6m)^(2)-4.1(9m^(2)-2m+2)ge0implies8m-8ge0`
`:.mge1` or `m epsilon[1,oo)`……..i
(ii) Consider `af(3)ge0`
`1.(9-18m+9m^(2)-2m+2)gt0`

`implies9m^(2)-20m+11gt0`
`implies(9m-11)(m-1)gt0`
`implies(m-11/9)(m-1)gt0`
`implies(m epsilon(-oo,1)uu(11/9,oo)`........ii
(iii) Consider `(-b/(2a)gt3)`
`(6m)/2gt3`
`impliesmgt1`
`impliesm epsilon (1,oo)`.......iii
Hence the values of `m` satisfied Eq. i, ii and iii at the same time are `m epsilon (11/9,oo)`