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Simplify (2^1/2 - 2^-1/2)^2 ill write it neater. Please help

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i know formula a^2 - 2ab + b^2
i dont get it :P

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|dw:1359872887253:dw|btw original question is
thats original quesiton
yes your right now hartnn :)
can you simplify that now ?
answer 5?
is there a way to do this question using indices laws?
cause my teacher prefers that :P
yes, 5 is correct.
i have used law od indices \(2^{1/2}.2^{1/2}= 2^{1/2+1/2}=2^1=2\)
got that^ ?
yes thank you so much
welcome ^_^
\[(2^{1/2} - 2^{-1/2})^2 = (2^{1/2}-2^{-1/2})(2^{1/2}-2^{-1/2})=\]\[2^{1/2}*2^{1/2}-2^{-1/2}2^{1/2} - 2^{-1/2}2^{1/2} + 2^{-1/2}2^{-1/2} = \]\[2^1-2^0-2^0+2^{-1} = 2 - 1 - 1 + \frac{1}{2} = \frac{1}{2}\]
Maybe easier to write \(a = 2^{1/2}\) and \(b = a^{-1/2}\) then \[(a-b)^2 = a^2 - 2ab + b^2 = (2^{1/2})^{1/2} - 2*2^{1/2}*2^{-1/2} + (2^{-1/2})^2 =\]\[2^1 - 2*2^0 + 2^{-1} = 2^{-1} = \frac{1}{2}\] and use some different properties :-)

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