Question

Oblicz x^3- 1/x^3 , wiedząc, że x- 1/x =4

Answer 1

X³-1/x³=(x-1/x)(x²-x*1/x+1/x²)=(x-1/x)(x²-1+1/x²)

x-1/x=4  /()²
x²-2*x*1/x+1/x²=4
x²+1/x²=4+2
(x³-1/x³)=4*(6-1)=4*5=20