How do you solve: x^3/2=125?

1 Answer

x=5root[3]2, \ 5\root[3]2e^{i{2\pi}/3},\ 5\root[3]2e^{i{4\pi}/3}

Explanation:

x^3/2=125

x^3=125\cdot 2

x^3=250

x^3=250e^{i0}

x^3=250e^{i2k\pi}

x=(250e^{i2k\pi})^{1/3}

x=\root[3]{250}e^{i{2k\pi}/3}

x=5\root[3]{2}e^{i{2k\pi}/3}

Where, k=0, 1, 2

Now, setting the values of k, we get three roots of given cubic equation as follows

x=5root[3]2, \ 5\root[3]2e^{i{2\pi}/3},\ 5\root[3]2e^{i{4\pi}/3}