Question

find x³+1/x³ if X =9-4√5​

Answer 1

Answer:

5796

Step-by-step explanation:

   x = 9 - 4√5

∴  1/x = 1/(9-4√5)

         = (9+4√5)/(9+4√5)(9-4√5)

         = (9 + 4√5)                         [∵ 9² - (4√5)² = 81-80 = 1]

now, x³+1/x³ = (x + 1/x) (x²+1/x² - x*1/x)

                    = (9 - 4√5 + 9 + 4√5) [ (x + 1/x)² - 2]

                    = 18 [ (9 - 4√5 + 9 + 4√5)² -2 ]

                    = 18 [ 18² - 2]

                    = 18 [324 - 2] = 18 x 322 = 5796