grandes-ecoles 2025 Q36

grandes-ecoles · France · centrale-maths1__official Stationary points and optimisation Prove an inequality using calculus-based optimisation
Show that
$$\forall ( x , y ) \in ] 0,1 \left[ ^ { 2 } , \quad \frac { x ( 1 - x ) y ( 1 - y ) } { 1 - x y } \leqslant \frac { 5 \sqrt { 5 } - 11 } { 2 } \right.$$
Show that

$$\forall ( x , y ) \in ] 0,1 \left[ ^ { 2 } , \quad \frac { x ( 1 - x ) y ( 1 - y ) } { 1 - x y } \leqslant \frac { 5 \sqrt { 5 } - 11 } { 2 } \right.$$