Solve for x : x^3 = 243
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justaguide
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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)
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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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