Minimize $Q=2 x^{2}+5 y^{2}$, where $x+y=7$. \[ \begin{array}{l} x=\square \\ y=\square \end{array} \]

Step 1 ：Define the Lagrange function as \(L(x, y, \lambda) = 2x^2 + 5y^2 - \lambda(x + y - 7)\).

Step 2 ：Find the partial derivatives of L with respect to x, y, and \(\lambda\), and set them equal to zero. This gives us the following equations: \(4x - \lambda = 0\), \(10y - \lambda = 0\), and \(-x - y + 7 = 0\).

Step 3 ：Solve the system of equations to find the values of x, y, and \(\lambda\). The solution is \(x = 5\), \(y = 2\), and \(\lambda = 20\).

Step 4 ：Substitute these values back into the original equation to verify that they satisfy the constraint \(x + y = 7\).

Step 5 ：Final Answer: \(x = \boxed{5}\), \(y = \boxed{2}\)