Question

if x^2+1/x=82/9 then x^3 - 1/x^3 find the value .

Answer 1

x^2 +1/x^2 =83, => (x+1/x)^2 -2x.1/x =83

or, (x+1/x)^2 = 83+2 =85

or, (x+1/x) = ±√(85)

Now, x^3 + 1/x^3= (x+1/x)^3 -3*x*1/x(x+1/x)

=> (±√85)^3 - 3*(±√85) = 82√85 , - 82√85