Mathematics
13 Online
OpenStudy (itsmichelle29):
help
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OpenStudy (alexandervonhumboldt2):
solve:
64b^2+49=0
OpenStudy (alexandervonhumboldt2):
64=8*8
49=7*7
so basicly this is the diffrence of complex roots
OpenStudy (alexandervonhumboldt2):
difference of squares of complex roots
TheSmartOne (thesmartone):
Hint:
\(\sf\Huge a^2 + b^2 = (a+bi)(a-bi)\)
OpenStudy (alexandervonhumboldt2):
yeah
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TheSmartOne (thesmartone):
:)
OpenStudy (itsmichelle29):
so A
OpenStudy (alexandervonhumboldt2):
yeah
TheSmartOne (thesmartone):
nope
OpenStudy (itsmichelle29):
thanks
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TheSmartOne (thesmartone):
you lost the `i`
OpenStudy (alexandervonhumboldt2):
wait
TheSmartOne (thesmartone):
it's not A
OpenStudy (alexandervonhumboldt2):
HHAHA i did lost it too omg
OpenStudy (alexandervonhumboldt2):
you forgot about i
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OpenStudy (itsmichelle29):
so D
TheSmartOne (thesmartone):
Hint:
\(\sf\Huge a^2 + b^2 = (a+b\color{red}{i})(a-b\color{red}{i})\)
OpenStudy (alexandervonhumboldt2):
yes
TheSmartOne (thesmartone):
yup :)
OpenStudy (alexandervonhumboldt2):
D is correct
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TheSmartOne (thesmartone):
Good job @AlexandervonHumboldt2 and @itsmichelle29 :)
OpenStudy (itsmichelle29):
y the i
OpenStudy (itsmichelle29):
n.m. i get it lol
TheSmartOne (thesmartone):
you see the a^2 + b^2 formula is not the same as a^2 - b^2 formula
a^2 - b^2 = (a+b)(a-b)
TheSmartOne (thesmartone):
Answer choice A is based off of the a^2 - b^2 formula
not the a^2 + b^2 formula
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OpenStudy (alexandervonhumboldt2):
you cannot factor a^2-b^2 using rational values
OpenStudy (alexandervonhumboldt2):
wioops
OpenStudy (alexandervonhumboldt2):
i meant a^2+b^2
OpenStudy (alexandervonhumboldt2):
you have to use complex numbers
TheSmartOne (thesmartone):
Let's cross multiply
\(\sf\LARGE (a+b\color{red}{i})(a-b\color{red}{i})=a^2+abi -abi -(bi)^2\\\\\LARGE a^2 - (bi)^2 = a^2 -(b^2)(i^2) = a^2 - (b^2)(-1) = \\\\\Large\boxed{a^2 + b^2} \)
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TheSmartOne (thesmartone):
do you understand? :)