Question 51
Find the maximum and the minimum values of
$$
S = (1 - x_{1})(1 - y_{1}) + (1 - x_{2})(1 - y_{2})
$$
for real numbers $x_{1}, x_{2}, y_{1}, y_{2}$ with $x_{1}^{2} + x_{2}^{2} = y_{1}^{2} + y_{2}^{2} = 2013$.
$$
S = (1 - x_{1})(1 - y_{1}) + (1 - x_{2})(1 - y_{2})
$$
for real numbers $x_{1}, x_{2}, y_{1}, y_{2}$ with $x_{1}^{2} + x_{2}^{2} = y_{1}^{2} + y_{2}^{2} = 2013$.