Given a^2 + b^2 = 234 and ab = 108, compute the ratio (a + b) / (a − b). Provide the exact simplified value.

Introduction / Context:
Here you are given symmetric information about two unknowns: sum of squares and product. The task is to deduce (a + b)/(a − b) without solving for a and b individually, by using identities for squared sums and differences.

Given Data / Assumptions:

• a^2 + b^2 = 234.
• ab = 108.
• Assume a ≠ b so that a − b ≠ 0.

Concept / Approach:
Use (a + b)^2 = a^2 + b^2 + 2ab and (a − b)^2 = a^2 + b^2 − 2ab to find the magnitudes of (a + b) and (a − b). The ratio of the square roots then simplifies cleanly.

Step-by-Step Solution:

Verification / Alternative check:
If desired, construct numbers with these invariants (for instance via solving t^2 − (a + b)t + ab = 0) and verify the ratio numerically; it will still reduce to 5.

Why Other Options Are Wrong:
10, 8, 4, and 6 do not respect the exact square-root simplifications from the given invariants.

Common Pitfalls:
Forgetting factors of 2 in the identities or attempting to solve for a and b explicitly, which is unnecessary and time-consuming.

Final Answer:
5