Question

x^2+1/x^2=82/9 then x^3-1/x^3​

Answer 1

Step-by-step explanation:

x^2+1/x^2=82/9

(x-1/x)^2+2(x)(1/x)=82/9

(x-1/x)^2=(82/9)-2

(x-1/x)^2=(82-18)/9

(x-1/x)=_/(64/9)

(x-1/x)=8/3

Now

x^3-1/x^3=(x-1/x)(x^2+1/x^2+x*1/x)

=(8/3)((82/9)+1)

=(8*91)/(3*9)

=728/27

x^3-1/x^3=728/27