Question

plz Ans this

if x+1/x=4 find x^3-1/x^3

Answer 1

since

x+1/x =4,

then
(x+1/x)²=4²,

x²+1/x² + 2 = 16

then
x²+1/x²=16-2=14,

hence

(x-1/x)²=x²+1/x²-2,

(x-1/x)²=14-2=12,

(x-1/x) = √12=2√3,

therefore

x³-1/x³,

(x-1/x) (x²+1/x²+1),

2√3 × (14+1),

30√3