Question

If X²+1/x²=51 then what is the value of x³-1/x³

Answer 1

x² + (1/x²) = 51

x² + (1/x²) = 2 + 49

x² + (1/x²) - 2 = 49

(x - 1/x)² = 49

x - 1/x = 7

Now,

x³ - (1/x³)

= (x - 1/x)³ + 3(x - 1/x)

= 7³ + 3 * 7

= 343 + 21

= 364

Hope it help!