Minimum Value of Algebraic Expression

Expand the expression: $E = 2601 \left(1 + \frac{1}{x} + \frac{1}{y} + \frac{1}{xy}\right) = 2601 \left(1 + \frac{x+y}{xy} + \frac{1}{xy}\right)$ Since $x + y = 102$, $xy$ is maximized when $x = y = 51$. Max value of $xy = 51 \times 51 = 2601$. To minimize $E$, we need to minimize $\frac{103}{xy} + 1$, which occurs when $xy$ is maximum, i.e., $xy = 2601$. Substitute $xy = 2601$: $E_{\text{min}} = 2601 \left(1 + \frac{102}{2601} + \frac{1}{2601}\right) = 2601 + 102 + 1 = 2704$