let p,q,r belongs to positive real no and2/pqr>=(p+q+r)^3 and 3p+4q+5r=12 then p^3+q^4+r^5 is equal to

There is an error in the question. Please check the first expression and reply with correct question. Amit Jain IIT Delhi AskIITian Faculty

let p,q,r belongs to positive real no and and27pqr>=(p+q+r)^3 and 3p+4q+5r=12 then p^3+q^4+r^5 is equal to

Use the concept of AM>=GM. so p+q+r/3 >= (pqr)^1/3. So by this and the relation given in the question, we can deduce that equality holds when p=q=r=1. So the value of given expression would be 3. Hope that helps. Amit Jain IIT Delhi AskIITians Faculty