#Been asked to solve cubic root of (729)

47 messages · Page 1 of 1 (latest)

balmy storm
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It is harder than you may think #1020426321261756536

rose bobcatBOT
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balmy storm
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Note: tartaglia's formula doesn't seem to help

civic canyon
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Well 810-81=729

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So 729=81 * 10-81=9 * 81

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=9^3

raven flare
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or just prime factorize 729…?

balmy storm
balmy storm
raven flare
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???

balmy storm
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Cubic root of (729) is not exactly 9

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Cubic root of (729) = x

civic canyon
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Do you want the complex solutions as well ?

balmy storm
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I want the work out

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Like a tip

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Or something

civic canyon
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Okay well x^3=729 so (x/9)^3=1

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Let z=x/9

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You have z^3=1

balmy storm
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Ok

civic canyon
balmy storm
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I really strugle with those

civic canyon
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Hmmm well 1= e^(2kipi)

balmy storm
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-9i isnt an answer right?

civic canyon
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Nope

balmy storm
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Give me only 1 tip

civic canyon
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All the solutions of z^3=1 are of the form e^(2kipi/3) with k in{0,1,2}

balmy storm
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Alr so

civic canyon
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Also the cubic root of something is unique you should’ve said solve the equation x^3=729

balmy storm
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1, (e^{(2i\pi/3)}), and (e^{(4i\pi/3)}).

stoic vaporBOT
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/🤍Byte Benders🤍™/ Katie

982294998248718377.png
balmy storm
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?

civic canyon
balmy storm
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Wow

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Ty 😃

civic canyon
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And e^(4ipi/3) is the conjugate of e^(2ipi/3)

civic canyon
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Remember though z=(x/9)

balmy storm
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Yk 1 = x/9 then

civic canyon
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Yes 1=x/9, e^(2ipi/3)=x/9 or e^(4ipi/3)=x/9

balmy storm
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Have a good one ❤️

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Ima dip

civic canyon