Inequalities
AM-GM Inequality
MMTS_Full_Test_13
Grade 12
Question:
Let $p,q,r$ are positive real numbers, such that $27pqr\ge(p+q+r)^3$ and $3p+4q+5r=12$, then $p^3+q^4+r^5=$
Step-by-Step Solution
Key Concept: Equality in AM-GM holds when $p=q=r$; use the constraint
Equality when $p=q=r$. $3p+4p+5p=12\Rightarrow p=1$. $p^3+q^4+r^5=1+1+1=3$.
Correct Answer: 1