Question

If a₁, a₂ …….. a_n are positive real numbers whose product is a fixed number c, then the minimum value of a₁ + a₂ + … a_{n – 1} + 2 a_n is –

• A. n(2c)^1/n
• B. (n + 1) c^1/n
• C. 2 nc^1/n
• D. (n + 1) (2c)^1/n

Answer 1

Answer: (A)

n(2c)^1/n

Answer 2

a₁, a₂, a₃ …… a_n = c ̃ a₁ a₂ a₃ … a_{n – 1} (2a_n) = 2c

Q AM ³ GM

$\frac { \mathrm { a } _ { 1 } + \mathrm { a } _ { 2 } + \mathrm { a } _ { 3 } + \ldots \mathrm { a } _ { \mathrm { n } - 1 } + 2 \mathrm { a } _ { \mathrm { n } } } { \mathrm { n } }$ ³ (a₁ a₂ a₃ … 2a_n)^1/n

a₁ + a₂ + a₃ + … a_{n – 1} + 2a_n ³ n(2c)^1/n