Question

x²+1/x²=82/9 then x³-1/x³ what​

Answer 1

We know,

(x−1/x)²=x²+1x²−2 -->{i}

x²+1/x²=82/9 -->{ii}

From (i)

=>(x−1/x)²=82/9−2 {using (ii) }

=>(x−1/x)²=64/9

=>(x−1/x)=8/3

Also,

=>(x³−1/x³)=(x−1/x)(x²+1/x²+1)

=>(x³−1/x³)=(8/3)(82/9+1)

=>(x³−1/x³)=(8/3)(91/9)

=>(x³−1/x³)=728/27