# Find the largest real solution

• Mar 6th 2010, 07:46 AM
nandokommando
Find the largest real solution
The largest real solution for x^2/3 - 5x^1/3 + 4 = 0 would be x =

For this one I only got two solutions, 64 and 1. I thought 64 was the correct answer but apparently I got something wrong. The real answer is 8, does anyone know what I did wrong here?
• Mar 6th 2010, 08:21 AM
VonNemo19
Quote:

Originally Posted by nandokommando
The largest real solution for x^2/3 - 5x^1/3 + 4 = 0 would be x =

For this one I only got two solutions, 64 and 1. I thought 64 was the correct answer but apparently I got something wrong. The real answer is 8, does anyone know what I did wrong here?

Let $u=x^{1/3}$, then we have

$u^2-5u+4=0$

$(u-4)(u-1)=0\Rightarrow{u}=1,4\Rightarrow{x}=1,64$.