When does the equality occurs?

Algebra Level 3

By A M − G M AM-GM , we have

a + 2 b + 3 c ≥ 3 6 a b c 3 a+2b+3c\geq3\sqrt[3]{6abc}

When does the equality occurs?

a = 2 b = 3 c a=2b=3c a = b = c a=b=c Equality does not occur. a = b 2 = c 3 a=\frac{b}{2}=\frac{c}{3}

Christopher Boo by Christopher Boo , 24, Singapore

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1 solution

Edwin Gray
Sep 23, 2018

If a = 2b = 3c, the left side is a + a + a = 3a. The right side is 3 (6 a (a/2) (a/3))^(1/3) = 3a. Ed Gray

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