Thread: Solving an inequality

Let x and y be positive real numbers. Prove that:



I'm not sure how to approach this. Do I simplify/expand somehow or is there a special thing I should do with problems like these.

Please help, thanks, BG

Use AM-GM inequality:







Now multiply the inequalities.

Originally Posted by BG5965

Let x and y be positive real numbers. Prove that:



I'm not sure how to approach this. Do I simplify/expand somehow or is there a special thing I should do with problems like these.

Please help, thanks, BG

Hello there is the solution:
I'have :


but :










^2 q + q^2 p + 4\left( {p + q} \right) + 2\left( {p^2 + q^2 } \right) \ge 8pq + 4pq" alt="(1) + (2)^2 q + q^2 p + 4\left( {p + q} \right) + 2\left( {p^2 + q^2 } \right) \ge 8pq + 4pq" />
Conclusion :

Sorry, dhiab, but I don't 100% understand your post - especially everything after step 1 (the expansion). E.g. why is suddenly and everything after that.

Could you please explain further. Thanks, BG