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Problem 10 - Entrance Test

If x - 1/x = 3, find the value of x^3 - 1/x^3.

Correct: B

Given x - 1/x = 3. Cube both sides: (x - 1/x)^3 = 3^3 Using (a-b)^3 = a^3 - b^3 - 3ab(a-b), with a = x and b = 1/x. x^3 - (1/x)^3 - 3(x)(1/x)(x - 1/x) = 27 x^3 - 1/x^3 - 3(1)(3) = 27 x^3 - 1/x^3 - 9 = 27 x^3 - 1/x^3 = 27 + 9 x^3 - 1/x^3 = 36.