Question

If x-1/x=4,find x^2+1/x^2;x^3-1/x^3

Answer 1

Step-by-step explanation:

x-1/x=4

squaring on both sides

(x-/x)^2=4^2

x^2+1/x^2-2.x.1/x=16

x^2+1/x^2=16+2

x^2+1/x^2=18

similarly

cubing on both sides we get

(x-1/x)^3=4^3

x^3-1/x^3-3.x.1/x(x-1/x)=64

x^3-1/x^3-3(4)=64

x^3-1/x^3=64+12

x^3-1/x^3=78