Question

Question #d8979

Answer 1

`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`