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a,b,c

by shashank.ism » Sat Feb 06, 2010 8:39 am
If (a^2)(b^3)(c) = 256/27 then find the minimum value of (a + b + c), where a, b and c are positive real numbers.

a.) 3
b.) 4
c.) 6
d.) 9
e.) 12

The OA is b
Anyone please explain the steps, how to solve this problem..
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by outreach » Sat Feb 06, 2010 12:33 pm
Min value of a+b + c will be attained when a/2 = b/3 = c ( say k)

a = 2k, b = 3k, c = k

4* 27 k6 = 256 / 27

k6 = 256 / (4*27*27) = 26 / 36

k = 2/3

(a+b+c)min = 6k = 4
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