Let

Then

The constraint becomes

so

Also,

Hence

Now rewrite $$$P$$$:

Since $$$b^2\ge0$$$ and

we get

Put

Then

so

Finally,

hence

It remains to check that equality is attainable.

Equality requires

Thus

so

Taking

with the same sign gives $$$b=0$$$, hence $$$x=y=a$$$.

These values satisfy the original constraint, so the bound is attained.

Therefore,

is the minimum value of the expression

#include<bits/stdc++.h>
using namespace std;

int main() {
    double c=12;
    double u=sqrt(c)/2;
    cout<<u*u-sqrt(c)*u<<'\n';
}