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Let a > 0, b > 0, c > 0 with 2a + b + 3c = 1. When the expression a⁴ * b² * c² is maximized, find the value of 1/a + 1/b + 1/c.

1. 18
2. 20
3. 22
4. 24

Correct answer: 20

Solution

AM-GM on the 8 terms a/2, a/2, a/2, a/2, b/2, b/2, 3c/2, 3c/2 (summing to 2a+b+3c=1) gives the maximum of a⁴*b²*c², attained when a=b=1/4, c=1/12, giving 1/a+1/b+1/c = 4+4+12 = 20.

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