Test

Test

Open Ended

1. Positive real numbers  $a$  and  $b$  satisfy  $a+\frac{1}{b}=7$  and  $b+\frac{1}{a}=5$  . Compute  $ab+\frac{1}{ab}$  .

Solution to Problem 1

Multiply the two equations together to get  $\left(a+\frac{1}{b}\right)\left(b+\frac{1}{a}\right)=ab+1+1+\frac{1}{ab}=35\Longrightarrow ab+\frac{1}{ab}=33$