a, b and c are positive real numbers such th...
a, b and c are positive real numbers such that a + b + c = p, where 'p' is a constant. Find the maximum value of (p - a) (p - b)(p - c).
• a)
(p3 - abc)
• b)
8p3/27
• c)
5p3/16
• d)
9p3/8
a, b and c are positive real numbers such that a + b + c = p, where '...
(p − a), (p − b) and (p − c) all are positive numbers.
∴ AM ≥ GM Hence (b) is the correct answer.
Alternative Method:
(p − a) + (p − b) + (p − c) = 2p(constant)
⇒ (p − a)⋅(p − b)⋅(p − c) will be maximum when
p − a = p − b = p − c = 2p/3
Maximum value of the product 1 Crore+ students have signed up on EduRev. Have you?
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