Question

the value of x + 3 e cube + X - 3 cube is is​

Answer 1

Answer:

The answer is zero

(x+1/x)^2 =3

Taking root on both side that makes

(x+1/x)=√3……case 1

Now lets take cube on both side

(x+1/x)^3=(√3)^3

x^3 +1/x^3 + 3*x^2*1/x + 3*x*1/x^2=3*√3

x^3 + 1/x^3 + 3*x+ 3*1/x=3*√3

x^3 + 1/x^3+3*(x+1/x)=3*√3

From case 1 we know that x+1/x =√3

Therefore replacing x+1/x in equation we get

x^3 + 1/x^3 + 3*(√3)=3*√3

Taking 3*√3 on right side we get

x^3 + 1/x^3 = 3√3 - 3√3

Therfore

x^3+1/x^3=0