Solve Equations For y

harpazo

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TheJason

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1.

\(\displaystyle y^{5} = 125\)

\(\displaystyle \sqrt[5]{y^{5}} = \sqrt[5]{125}\)

\(\displaystyle y = 5\)

However, there might be some nth root stuff. But this is the way it seemingly goes.

2.

\(\displaystyle y^{6} = 100\)

\(\displaystyle \sqrt[6]{y^{6}} = \sqrt[6]{100}\)

\(\displaystyle y = ?\)

Again, quite sure the answer is something more than one number
 
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harpazo

Pure Mathematics
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1.

\(\displaystyle y^{5} = 125\)

\(\displaystyle \sqrt[5]{y^{5}} = \sqrt[5]{125}\)

\(\displaystyle y = 5\)

However, there might be some nth root stuff. But this is the way it seemingly goes.

2.

\(\displaystyle y^{6} = 100\)

\(\displaystyle \sqrt[6]{y^{6}} = \sqrt[6]{100}\)

\(\displaystyle y = ?\)

Again, quite sure the answer is something more than one number
I'm sure there is missing work in your reply. I give you credit for trying. Let Mark take it from here.
 

MarkFL

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\(\displaystyle y^5=125\left(\cos(2\pi k)+i\sin(2\pi k)\right)\)

By de Moivre:

\(\displaystyle y=5^{\Large\frac{3}{5}}\left(\cos\left(\frac{2\pi}{5}k\right)+i\sin\left(\frac{2\pi}{5}k\right)\right)\) where \(\displaystyle k\in\{0,1,2,3,4\}\)
 
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harpazo

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\(\displaystyle y^5=125\left(\cos(2\pi k)+i\sin(2\pi k)\right)\)

By de Moivre:

\(\displaystyle y=5^{\Large\frac{3}{5}}\left(\cos\left(\frac{2\pi}{5}k\right)+i\sin\left(\frac{2\pi}{5}k\right)\right)\) where \(\displaystyle k\in\{0,1,2,3,4\}\)
Does de Moivre pop up in calculus 1?