Question

If x+ 1/x= 3. Find xsquare+1/xsquare and xcube+1/xcube

Answer 1

x+1/x=3,

(x+1/x)²=3²,

x²+1/x²+2=9,

then
x²+1/x²=7,

since
x+1/x=3,

then
(x+1/x)³=3³,

x³+1/x³+3(x+1/x)=27,

x³+1/x³+3×3=27,

then
x³+1/x³=27-9=18