What is x if x^3-1728=0?

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We are given that x^3 - 1728 = 0 and we have to find x.

x^3 - 1728 = 0

=> x^3 = 1728

=> x^3 = 12^3

As the exponent is the same, we can equate the bases

This gives x = 12.

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giorgiana1976 | Student

We notice that the number 1728 = 12^3.

We'll re-write the equation as a difference of squares:

x^3 - 12^3 = 0

We'll apply the formula:

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

x^3 - 12^3 = (x-12)(x^2 + 12x + 144)

If x^3 - 12^3 = 0 => (x-12)(x^2 + 12x + 144) = 0

We'll set each factor as zero:

x -12 = 0

x = 12

x^2 + 12x + 144 = 0

x1 = [-12+sqrt(144 - 576)]/2

Since sqrt-432 is not a real value, the equation has a single real solution.

The real solution of the equation is x = 12.

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