How do you solve: x^3/2=125? Algebra Quadratic Equations and Functions Comparing Methods for Solving Quadratics 1 Answer Harish Chandra Rajpoot Jul 5, 2018 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} Answer link Related questions What are the different methods for solving quadratic equations? What would be the best method to solve -3x^2+12x+1=0? How do you solve -4x^2+4x=9? What are the two numbers if the product of two consecutive integers is 72? Which method do you use to solve the quadratic equation 81x^2+1=0? How do you solve -4x^2+4000x=0? How do you solve for x in x^2-6x+4=0? How do you solve x^2-6x-16=0 by factoring? How do you solve by factoring and using the principle of zero products x^2 + 7x + 6 = 0? How do you solve x^2=2x? See all questions in Comparing Methods for Solving Quadratics Impact of this question 2881 views around the world You can reuse this answer Creative Commons License