1. ## Unusual equation

Hi!

How should one proceed with an equation like this..

x^(1/2) + x^(1/4) = 20

without having any calculator obv..

thanks!

2. let $\displaystyle y = x^{\frac{1}{4}}$

$\displaystyle y^2 + y - 20 = 0$

factor $\displaystyle (y+5)(y-4)=0$

can you take it form here?

3. ## hi

uh..
I understood what you did.

y = -5 or y = 4 ?

but.. do I get the correct answer?
If I insert 4 into the original equation..

4. Because $\displaystyle x^{\frac{1}{4}} = - 5$ is impossible the there is one solution.
$\displaystyle x^{\frac{1}{4}} = 4\quad \Rightarrow \quad x = 64$

5. ## hi

doesnt x = 256 ?

because 4^4 is 256

and sqrt of 256 is 16, so 16 plus 4 = 20

6. Originally Posted by Twig
doesnt x = 256 ?

because 4^4 is 256

and sqrt of 256 is 16, so 16 plus 4 = 20
Yes.

Plato made a simple careless mistake. Be that as it may, it's a mere detail - it's the method that's important and the method is what Plato's given you.

7. ## hi

Absolutely, the method is def. the most important.
Just wanted to be sure that I got it correct.

Thanks!