If product of the real roots of the equation, `x^(2)-ax+30=2sqrt((x^(2)-ax+45)),agt0` is `lamda` minimum value of sum of roots of the equation is `mu`. The value of `(mu)` (where (.) denotes the least integer function) is

Answer

9

Explanation

Let `x^(2)-ax+30=y`
`:.y=2sqrt(y+15)`…i
`impliesy^(2)-4y-60=0`
`implies(y-10)(y+6)=0`
`:.y=10,-6`
`impliesy=10,y!=-6 [ :' ygt0]`
Now `x^(2)-ax+30=10`
`impliesx^(2)-ax+20=0`
Given `alpha beta=lamda=20`
`:.(alpha+beta)/2gesqrt(alpha beta)=sqrt(20)`
`impliesalpha +beta ge2sqrt(2)`
or `mu=4sqrt(5)`
`:.` Minimum value fo `mu` is `4sqrt(5)`
i.e. `mu=4sqrt(5)=8.9implies(mu)=9`