# Algbra Problem

p,q and r are three non-negative integers such that p + q + r = 10. The maximum value of pq + qr + pr + pqr is

Note by Sandeep Sharma
4 years, 6 months ago

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First of all I would like to tell you that it is 'Algebra', Not 'Algbra' . For your question, I can give you a hint. You figure it out. we have to find maximum value of pq+qr+rp+pqr Divide and multiply this by pqr. So it becomes $$pqr(1/p+1/q+1/r+1)$$.Now by applying AM-GM inequality, find the maximum of pqr, Then use AM-HM inequality and fin maximum value of $$1/p+1/q+1/r$$ and that will lead you to the answer.

- 4 years, 6 months ago