Question

Find the value of x³ - 1/x³
if x²+1/x² = 18​

Answer 1

Answer:

Step-by-step explanation:

Given x^2 + 1/x^2 = 18.

         x^2 + 1/x^2 = 16 + 2

        x^2 + 1/x^2 - 2 = 16

        (x - 1/x)^2 = 16

       (x - 1/x) = 4.   ---- (1)

We know that a^3 - b^3 = (a-b)(a^2 + ab + b^2).

x^3 - 1/x^3 = (x - 1/x)(x^2 + x * 1/x + 1/x^2)

                 = (x - 1/x)(x^2 + 1 + 1/x^2)

                = 4 * (18 + 1) (From (1))

                = 4 * 19

                = 76.

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