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The minimum value of the sum of real numbers a -5 , a -4 , 3a -3 , 1, a 8 and a 10 where a > 0 is.

 The minimum value of the sum of real numbers a-5, a-4, 3a-3, 1, a8 and a10 where a > 0 is.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Sol. 8
∵ a > 0, ∴ a-5, a-4, 3a-3, 1, a8, a10 > 0
Using A M ≥ G M for positive real numbers we get
1/a5 + 1/a4 + 1/a3 + 1/a3 + 1/a3 + 1 + a8 + a10 / 8 ≥ (1/a5. 1/a4. 1/33. 1/a3. 1/a3. 1. a8. a10)1/8
⇒ 1 /a5 + 1/a4 + 3/a3 + 1 + a8 + a10 ≥ 8(1)1/8.

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