Question

If x^2+ 1/^2 = 83, find the value of x^3− 1/^3

Answer 1

Answer:

(x-1/x)² = x² + 1/x² -2

(x-1/x)² =83-2

(x-1/x)² = 81

(x-1/x) = √82

(x-1/x) = +- 9

so, for x³-1/x³

(x-1/x)³ = x³-1/x³ -3(x-1/x)

(9)³ = x³-1/x³-3(9)

729 =x³-1/x³ -27

729+27 = x³-1/x³

756 = x³-1/x³