user917
  • user917
Why (a+1/a)^2 + (b+1/b)^2 ≥ (1/2)*(a+b+1/a+1/b)^2 ? By which rule?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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raffle_snaffle
  • raffle_snaffle
so we have |dw:1378680858279:dw|
raffle_snaffle
  • raffle_snaffle
Is this series and sequence?
user917
  • user917
\[(a+\frac{1}{a})^{2} + (b+\frac{1}{b})^{2} \ge \frac{ 1 }{ 2 } (a + b + \frac{ 1 }{ a } + \frac{ 1 }{ b })^{2}\]

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raffle_snaffle
  • raffle_snaffle
Is this a true or false question?
user917
  • user917
I know its true but why? Is there any proof or theorem for that?
raffle_snaffle
  • raffle_snaffle
Is this series?
raffle_snaffle
  • raffle_snaffle
user you may have to wait for someone else.=( I am sorry
raffle_snaffle
  • raffle_snaffle
let me find someone
raffle_snaffle
  • raffle_snaffle
I can't show you any proofs or theorems until I understand what math this is?
user917
  • user917
its an inequality, a true or false question (analysis math)
user917
  • user917
\[a ^{2}+b ^{2} \ge \frac{ 1 }{ 2 } (a+b)^{2}\] is that true?
blockcolder
  • blockcolder
Apply Cauchy-Schwarz on the sequences \(a+\frac{1}{a}, b+\frac{1}{b}\) amd \(1,~ 1\) and you get \[\left(a+\frac{1}{a}+b+\frac{1}{b}\right)^2 \leq \left[\left(a+\frac{1}{a}\right)^2+\left(b+\frac{1}{b}\right)^2\right](1^2+1^2) \] which is equivalent to your statement.
raffle_snaffle
  • raffle_snaffle
sorry user i am not very good at analysis math.

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