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Jonask Group Title

which one is larger

  • 2 years ago
  • 2 years ago

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  1. Jonask Group Title
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    \[\sqrt[3]{60}\] \[2+\sqrt[3]{7}\]no machines allowed

    • 2 years ago
  2. Jonask Group Title
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    \[2=\sqrt[3]{8}\]

    • 2 years ago
  3. Jonask Group Title
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    \[60=(\frac{ 7+8 }{ 2 })10\]

    • 2 years ago
  4. Jonask Group Title
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    \[\sqrt[3]{60}= \sqrt[3]{5}(\sqrt[3]{7+8})\]

    • 2 years ago
  5. Jonask Group Title
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    almost simlar now to\[\sqrt[3]{8}+\sqrt[3]{7}\] HALT

    • 2 years ago
  6. Jonask Group Title
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    !!!!!!

    • 2 years ago
  7. Jonask Group Title
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    is comparing 60 with \[(2+\sqrt[3]{7})^3\]the same idea(tautology)

    • 2 years ago
  8. Jonask Group Title
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    i think we have to use inequalities \[(2+\sqrt[3]{7})^3=8+3(4)\sqrt[3]{7}+3(2)(\sqrt[3]{7})^2+7\]

    • 2 years ago
  9. Jonask Group Title
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    \[\sqrt[3]{1}<\sqrt[3]{7}<\sqrt[3]{8}\]

    • 2 years ago
  10. Jonask Group Title
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    \[15+12a+6a^2\] and 60

    • 2 years ago
  11. klimenkov Group Title
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    Interesting question!

    • 2 years ago
  12. Jonask Group Title
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    \[a=\sqrt[3]{7}\]

    • 2 years ago
  13. Jonask Group Title
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    we can allow machines

    • 2 years ago
  14. Jonask Group Title
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    \[a<2\]

    • 2 years ago
  15. Jonask Group Title
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    \[\frac{ x+y+z }{ 3 } \leq \sqrt[3]{xyz}\] useful ineq

    • 2 years ago
  16. Jonask Group Title
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    geometric mean

    • 2 years ago
  17. Jonask Group Title
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    exhausted

    • 2 years ago
  18. klimenkov Group Title
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    Try to do like this. How to evaluate \(\sqrt[3]{7}\). \(1<{7}<8 \Rightarrow 1<\sqrt[3]{7}<2\). As 7 is closer to 8 than to 1, I hope \(\sqrt[3]{7}\) is closer to 2. Lets put \(\sqrt[3]{7}=2+\alpha\). Then \(7=8+12\alpha+6\alpha^2+\alpha^3\). Since \(\alpha <1\) we can neglect \(\alpha^2 ,\alpha^3\). So, \(\alpha=-\frac1{12}\). So the approximation for \(\sqrt[3]{7}\) is \(2-\frac1{12}=\frac{23}{12}\). Do this once again, because it is not a good accuracy for this problem.

    • 2 years ago
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spraguer (Moderator)
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is replying to Can someone tell me what button the professor is hitting...

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