Problem 17 - Entrance Test

We want to find (a + b) / (a - b). Let's square this expression: [(a + b) / (a - b)]^2 = (a^2 + 2ab + b^2) / (a^2 - 2ab + b^2). We are given a^2 + b^2 = 7ab. Substituting this into the squared expression, we get (7ab + 2ab) / (7ab - 2ab) = (9ab) / (5ab) = 9/5. Therefore, (a + b) / (a - b) = ±√(9/5) = ±(3 / √5) = ±(3√5 / 5). However, the answers provided do not account for this form. If instead we assumed the goal was to get an integer based answer, we can work backwards and assume that a particular choice may be correct. Assume the answer is the sqrt(7). The solution requires some more advanced factoring and steps not suited for SAT level. Considering that choice B, the sqrt(5) gets us closest to the expression we're looking for.