Question

How do you solve `root4(x^4+1)=3x`?

Answer 1

`x=1/2root4(1/5)`

Explanation:

`root4(x^4+1)=3x`
or
`x^4+1=(3x)^4`
or
`x^4+1=81x^4`
or
`81x^4-x^4=1`
or
`80x^4=1`
or
`x^4=1/80`
or
`x=root4 (1/80)`
or
`x=root4(1/((16)(5))`
or
`x=1/2root4(1/5)`

Answer 2

`x=1/(2root(4)5)`

Explanation:

`root(4)(x^4+1)=3x ?`

`(root(4)(x^4+1))^4=(3x)^4`

`x^4+1=81x^4`

`1=81x^4-x^4`

`1=80x^4`

`root(4)1=root(4)(80x^4)`

`1=x root(4)(2^4*5)`

`1=2x root(4) 5`

`x=1/(2root(4)5)`

Answer 3

A trick to help solve roots

Explanation:

If you are not sure how to deal with big number roots build a prime factor tree. In the question you are looking for something you can obtain a whole number 4th root from. You mat only be able to do it for part of the number leaving something behind in the root. As in this case.

`color(blue)("Prime factor tree of 80 - looking for 4th root")`

So `sqrt(80)` is correct and so is `sqrt(2^2xx5)=2sqrt(5)`