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An inequality

Source: 1983 National High School Mathematics League, Exam One, Problem 6

February 21, 2020
inequalities

Problem Statement

Let a,b,c,d,m,na,b,c,d,m,n be positive real numbers. P=ab+cd,Q=ma+nc⋅bm+dnP=\sqrt{ab}+\sqrt{cd},Q=\sqrt{ma+nc}\cdot\sqrt{\frac{b}{m}+\frac{d}{n}}. Then (A)P≥Q(B)P≤Q(C)P<Q(D)\text{(A)}P\geq Q\qquad\text{(B)}P\leq Q\qquad\text{(C)}P<Q\qquad\text{(D)}Not sure
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