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justaguide eNotes educator| Certified Educator

We have to solve for x: x^3 = 243

x^3 = 243

=> x^3 = 27 * 9

=> x^3 = 3^3 * 3^2

=> x = 3* 3^(2/3)

The required value is x = 3*3^(2/3)

giorgiana1976 | Student

We'll solve the equation using the difference of cubes formula:

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

We'll write 243 = 9*3^3

x^3 - 9*3^3 = {x - 3*[3^(2/3)]}(x^2 + 3x*[3^(2/3)] + 27[3^(1/3)])

x - 3*[3^(2/3)] = 0

The real solution of the equation is: x = 3*[3^(2/3)]

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