Question

Find the value of x^3 - 1/x^3, if (i) x-1/x = 6, (ii) x+1/x= root 29

Answer 1

(i) x³ - 1/x³ = (x-1/x)³ + 3(x-1/x)

               = (6)³ + 3(6)

               = 216 + 18

               = 234

(ii) first, we find x-1/x

(x-1/x)² = (x+1/x)² - (4*x*1/x)

         = (x+1/x)²-4

          =(√29)² - 4

          = 29-4

          = 25

∴ x - 1/x = ± 5

Now, x³ - 1/x³ = (x-1/x)³+3(x-1/x)

                      = (5)³+(3*5)

                      = 125 +15

                     = 140, when x = 5.

And,

x³-1/x³ = (-5)³ +3(-5)

          = -125-15

          = -140, when, x = -5

Answer 2

Refer to the attachment...

Hope this will help you.

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