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Mathematics 13 Online
OpenStudy (itsmichelle29):

help

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

TheSmartOne (thesmartone):

:)

OpenStudy (itsmichelle29):

so A

OpenStudy (alexandervonhumboldt2):

yeah

TheSmartOne (thesmartone):

nope

OpenStudy (itsmichelle29):

thanks

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

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

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

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 \(\sf\LARGE (a+b\color{red}{i})(a-b\color{red}{i})=a^2+abi -abi -(bi)^2\\\\\LARGE a^2 - (bi)^2 = a^2 -(b^2)(i^2) = a^2 - (b^2)(-1) = \\\\\Large\boxed{a^2 + b^2} \)

TheSmartOne (thesmartone):

do you understand? :)

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