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TeemoTheTerific

  • 2 years ago

Hi... Last question and i can sleep peacefully :) THANKS

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  1. TeemoTheTerific
    • 2 years ago
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    \[\huge a= 2^{\frac{ 1 }{ 2 }} + 2^{\frac{ -1 }{ 2 }}\] \[\huge b=2^{\frac{ 1 }{ 2 }} - 2^{\frac{ -1 }{ 2 }}\] FIND \[\huge a ^{3} + b ^{3}\]

  2. TeemoTheTerific
    • 2 years ago
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    lol someone randomly gave me a medal?

  3. TeemoTheTerific
    • 2 years ago
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    i know the formula for a^3 + b^3 btw

  4. TeemoTheTerific
    • 2 years ago
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    (a+b)(a^2-ab + b^2)

  5. hartnn
    • 2 years ago
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    so, a+b=.. ?

  6. hartnn
    • 2 years ago
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    its actually \( 2 \times 2^{1/2}\)

  7. TeemoTheTerific
    • 2 years ago
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    yea :)

  8. hartnn
    • 2 years ago
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    ok, keep that as it is... now try (a^2-ab + b^2) =... ?

  9. TeemoTheTerific
    • 2 years ago
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    same thing as 2^1/2 + 2^1/2

  10. TeemoTheTerific
    • 2 years ago
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    i worked out a^2 was 9/2 before

  11. hartnn
    • 2 years ago
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    9/2 ? just a second..

  12. TeemoTheTerific
    • 2 years ago
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    b^2 was also ummm 1/2

  13. hartnn
    • 2 years ago
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    \((a^2-ab+b^2 )= (a^2-2ab+b^2)+ab = (a+b)^2+ab\) you already know a+b

  14. hartnn
    • 2 years ago
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    find ab

  15. hartnn
    • 2 years ago
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    we know a+b = 2*2^(1/2)

  16. TeemoTheTerific
    • 2 years ago
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    ab = 3/2?

  17. hartnn
    • 2 years ago
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    yes :)

  18. TeemoTheTerific
    • 2 years ago
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    would it be (a-b)^2 + ab? instead of (a+b)^2 + ab

  19. hartnn
    • 2 years ago
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    sorry, my mistake

  20. hartnn
    • 2 years ago
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    \((a^2-ab+b^2 )= (a^2+2ab+b^2)-3ab = (a+b)^2-3ab\)

  21. TeemoTheTerific
    • 2 years ago
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    so ill just work out (a^2-ab + b^2) manually?

  22. TeemoTheTerific
    • 2 years ago
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    wait but i dont think i done (a+b)^2

  23. hartnn
    • 2 years ago
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    i was just trying to simplify...you can do that manually, but it'll become complicated...

  24. TeemoTheTerific
    • 2 years ago
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    (a+b)^2 would be 8?

  25. hartnn
    • 2 years ago
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    yes. ab = 3/2 so, -3ab = -9/2 and 8+9/2 =... ?

  26. hartnn
    • 2 years ago
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    *8-9/2=..

  27. TeemoTheTerific
    • 2 years ago
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    7/2

  28. TeemoTheTerific
    • 2 years ago
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    so answer is (2^1/2 times 2 )(7/2) Is it?

  29. hartnn
    • 2 years ago
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    \(2 \times 2^{(1/2)} \times 7/2 =2^{(1/2)} \times 7 \)

  30. TeemoTheTerific
    • 2 years ago
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    ok thank you so much

  31. TeemoTheTerific
    • 2 years ago
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    these question confuse me so much :(

  32. hartnn
    • 2 years ago
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    practice more.... all confusions will go away...

  33. TeemoTheTerific
    • 2 years ago
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    lol thats easy to say

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