I need a help to find k here:

$f(x)=-k^x + x^2$


It is not too simple. I have interest to find the single value of "k" where, inside interval {x,2,3}, the function have only one value to x when f(x) = 0.

In fact, using try and error I have already found the value:

    ratio = -2.0870652286345332^x + x^2

    Plot[ratio, {x, 2.715, 2.720}] 

    FindMaximum[ratio, {x, 2.715, 2.720}]

    NSolve[ratio == 0 && x >= 2, x]


![XK Graph][1]

I need to know, a better way to reach the value `-2.0870652286345332` to `k`. Optimization? Solving? I was unable to got it.

Any insight are welcome.

Best regards

  [1]: https://i.sstatic.net/AZJtG.jpg