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

Mathematics
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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 \[\huge a ^{3} + b ^{3}\]
lol someone randomly gave me a medal?
i know the formula for a^3 + b^3 btw

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Other answers:

(a+b)(a^2-ab + b^2)
so, a+b=.. ?
its actually \( 2 \times 2^{1/2}\)
yea :)
ok, keep that as it is... now try (a^2-ab + b^2) =... ?
same thing as 2^1/2 + 2^1/2
i worked out a^2 was 9/2 before
9/2 ? just a second..
b^2 was also ummm 1/2
\((a^2-ab+b^2 )= (a^2-2ab+b^2)+ab = (a+b)^2+ab\) you already know a+b
find ab
we know a+b = 2*2^(1/2)
ab = 3/2?
yes :)
would it be (a-b)^2 + ab? instead of (a+b)^2 + ab
sorry, my mistake
\((a^2-ab+b^2 )= (a^2+2ab+b^2)-3ab = (a+b)^2-3ab\)
so ill just work out (a^2-ab + b^2) manually?
wait but i dont think i done (a+b)^2
i was just trying to simplify...you can do that manually, but it'll become complicated...
(a+b)^2 would be 8?
yes. ab = 3/2 so, -3ab = -9/2 and 8+9/2 =... ?
*8-9/2=..
7/2
so answer is (2^1/2 times 2 )(7/2) Is it?
\(2 \times 2^{(1/2)} \times 7/2 =2^{(1/2)} \times 7 \)
ok thank you so much
these question confuse me so much :(
practice more.... all confusions will go away...
lol thats easy to say

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