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The minimum value of the sum of real numbers { a }^{ -5 }+{ a

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The minimum value of the sum of real numbers $a^{- 5} + a^{- 4} + 3 a^{- 3}, 1, a^{8}$ and $a^{10}$ with $a > 0$ is

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The minimum value of the sum of real numbers

a^{- 5} + a^{- 4} + 3 a^{- 3}, 1, a^{8}

and

a^{10}

with

a > 0

11 mins ago

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11 mins ago

Text solutionVerified

Using

A . M \geq G . M

\Rightarrow \frac{a ^{- 5} + a ^{- 4} + a ^{- 3} + a ^{- 3} + a ^{- 3} + a ^{8} + a ^{10} + 1}{8} \geq 1

\Rightarrow a^{- 5} + a^{- 4} + a^{- 3} + a^{- 3} + a^{- 3} + a^{8} + a^{10} + 1 \geq 8

\Rightarrow (a^{- 5} + a^{- 4} + a^{- 3} + a^{- 3} + a^{- 3} + a^{8} + a^{10} + 1)_{min} = 8

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Question Text	The minimum value of the sum of real numbers $a^{- 5} + a^{- 4} + 3 a^{- 3}, 1, a^{8}$ and $a^{10}$ with $a > 0$ is
Answer Type	Text solution:1
Upvotes	150