If a and b are two unequal positive numbers, then:

smc

algebra senior

Problem

a

and

b

are two unequal positive numbers, then:

(A)

\frac{2 ab}{a + b} > s q r t (ab) > \frac{a + b}{2}

(B)

s q r t (ab) > \frac{2 ab}{a + b} > \frac{a + b}{2}

(C)

\frac{2 ab}{a + b} > \frac{a + b}{2} > s q r t (ab)

(D)

\frac{a + b}{2} > \frac{2 ab}{a + b} > s q r t (ab)

(E)

\frac{a + b}{2} > ab > \frac{2 ab}{a + b}

Solution

Using the RMS-AM-GM-HM inequality, we can see that the answer is

\frac{a + b}{2} > ab > \frac{2 ab}{a + b}

Final answer