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

3 Answers
Jul 31, 2016

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)

Jul 31, 2016

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)

Jul 31, 2016

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")
Tony BTony B

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