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.

Question

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.

Aditi Chauhan · Answer

Sol. 8 ∵ a > 0, &there4; a -5 , a -4 , 3a -3 , 1, a 8 , a 10 > 0 Using A M &ge; G M for positive real numbers we get 1/a 5 + 1/a 4 + 1/a 3 + 1/a 3 + 1/a 3 + 1 + a 8 + a 10 / 8 &ge; (1/a 5 . 1/a 4 . 1/3 3 . 1/a 3 . 1/a 3 . 1. a 8 . a 10 ) 1/8 &rArr; 1 /a 5 + 1/a 4 + 3/a 3 + 1 + a 8 + a 10 &ge; 8(1) 1/8 .

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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.

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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.

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