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



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TeemoTheTerific
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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
\[\huge a ^{3} + b ^{3}\]

TeemoTheTerific
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lol someone randomly gave me a medal?

TeemoTheTerific
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i know the formula for a^3 + b^3 btw

TeemoTheTerific
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(a+b)(a^2ab + b^2)

hartnn
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so, a+b=.. ?

hartnn
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its actually \( 2 \times 2^{1/2}\)

TeemoTheTerific
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yea :)

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

TeemoTheTerific
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same thing as 2^1/2 + 2^1/2

TeemoTheTerific
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i worked out a^2 was 9/2 before

hartnn
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9/2 ?
just a second..

TeemoTheTerific
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b^2 was also ummm 1/2

hartnn
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\((a^2ab+b^2 )= (a^22ab+b^2)+ab = (a+b)^2+ab\)
you already know a+b

hartnn
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find ab

hartnn
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we know a+b = 2*2^(1/2)

TeemoTheTerific
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ab = 3/2?

hartnn
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yes :)

TeemoTheTerific
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would it be (ab)^2 + ab? instead of (a+b)^2 + ab

hartnn
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sorry, my mistake

hartnn
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\((a^2ab+b^2 )= (a^2+2ab+b^2)3ab = (a+b)^23ab\)

TeemoTheTerific
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so ill just work out (a^2ab + b^2) manually?

TeemoTheTerific
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wait but i dont think i done (a+b)^2

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

TeemoTheTerific
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(a+b)^2 would be 8?

hartnn
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yes.
ab = 3/2
so, 3ab = 9/2
and 8+9/2 =... ?

hartnn
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*89/2=..

TeemoTheTerific
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7/2

TeemoTheTerific
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so answer is (2^1/2 times 2 )(7/2)
Is it?

hartnn
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\(2 \times 2^{(1/2)} \times 7/2 =2^{(1/2)} \times 7 \)

TeemoTheTerific
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ok thank you so much

TeemoTheTerific
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these question confuse me so much :(

hartnn
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practice more.... all confusions will go away...

TeemoTheTerific
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lol thats easy to say