Read Sum and sum-of-squares constraint
This IOQM pattern tests Discriminant/AM-QM bound for two real numbers. Identify the structure before calculating, then use the method below.
An inequality compares quantities under constraints; the equality condition tells whether a bound can be attained.
Find the structure
Identify the fixed quantity and the expression to bound before applying an inequality.
Build a valid route
Choose a bound whose equality condition can actually occur under the given constraints. Test that equality case separately.
Verify the conclusion
Return to the exact wording and test the final conclusion against every stated condition. A clean calculation is not enough if it solves a different problem.
OlympIQ exam lens
- ✓State what is fixed.
- ✓Apply a sharp bound.
- ✓Test the equality or extremal case.
A valid inequality may be too weak for the question; verify it gives the required sharp bound.
Ready to try the pattern?
100% coverage across the linked question.
Practise the linked question