Question #d8979

1 Answer
Oct 15, 2017

322

Explanation:

I shall assume you mean:

If x+1/x=3, then what is x^6+1/x^6?

Notice the following:

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

x^2+2*x*1/x+(1/x)^2=9

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

x^2+1/x^2=7

We can then cube both sides to get the power of 6 we are looking for.

(x^2+1/x^2)^3=7^3

(x^2)^3+3*(x^2)^2*1/x^2+3*x^2*(1/x^2)^2+(1/x^2)^3=343

x^6+3x^2+3*1/x^2+1/x^6=343

x^6+1/x^6+3(x^2+1/x^2)=343

However, if you remember from before, we know that x^2+1/x^2=7. We can plug that in to this equation:

x^6+1/x^6+3(7)=343

x^6+1/x^6=343-21

x^6+1/x^6=322