Question

If x(x-3)=-1 then the value of x3(x³-18) will be,​

Answer 1

Hi,

-1

Explanation:

if x(x-3)=-1 then x≠0 since

if x=0 then x(x-3))= 0*(0-3)=0 and not -1

`x\\eq 0 \\x(x-3)=-1 \Longrightarrow\ x-3=(-1)/(x) \Longrightarrow\ x+(1)/(x) =3\\\\\\(x+(1)/(x))^3\\=x^3+(1)/(x^3)+3*x^2*(1)/(x)+3*x*(1)/(x^2)\\=x^3+(1)/(x^3)+3*(x+(1)/(x))\\\\Hence\ x+(1)/(x) =3 \ thus\\\ 3^3=x^3+(1)/(x^3)+3*3\\x^3+(1)/(x^3)=27-9\\x^3+(1)/(x^3)=18\\\\x^3-18=-(1)/(x^3)\\\\\boxed{x^3*(x^3-18)=-1}\\`