Question

how to do this sum. can you tell me fast

Answer 1

x² + 1/x² = 66 ..............(1)

x² + 1/x² - 2*x*1/x  = 66 - 2*x*1/x

(x -1/x)² = 66 - 2 = 64

√(x-1/x)² = √64

x-1/x = 8 .....................(2)

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

x³ - 1/x³ = 8 (66 +1)

x³ - 1/x³ = 8 x 67 = 536