crossed ladder 더블릿

#include <stdio.h>
#include <algorithm>
#include <cmath>
 
using namespace std;
 
double root(double m, double x) {
    return sqrt(pow(m, 2) - pow(x, 2));
}
 
int main() {
    double m, n, h;
    scanf("%lf %lf %lf", &m, &n, &h);
 
    double left = 0, right = min(m, n),rst=0,mid;
    while (left < right) {        
        mid = (left + right) / 2;
        double result = h / root(m, mid) + h / root(n, mid) - 1;
        if (result <= 0) {
            if (left == mid)
                break;
            left = mid ;
 
        }
        else if (result > 0) {
            if (right == mid)
                break;            
            right = mid ;
        }
    }
    printf("%.3lf", mid);
}